What Is a Tensor?

What Is a Tensor? Gridspace 1.34K subscribers Subscribe 38 Share Ask Save 1,150 views Nov 15, 2024 #artificialintelligence #machinelearning #computerscience Gridspace Co-Founder and Co-Head of Engineering Anthony Scodary answers the question, "What is a Tensor?" as part of an ongoing series that hopes to shed some light on Machine Learning and Computer Science. Find out what a neural network is here: • What Is A Neural Network? #artificialintelligence #machinelearning #computerscience #ml Transcript Follow along using the transcript. Show transcript Gridspace 1.34K subscribers Videos About 3 Comments rongmaw lin Add a comment... @JuanPabloMolinaMatute 1 year ago I finally understood what a tensor really is :-) and it blew my mind 3 Reply Gridspace · 1 reply @DonMaximus73 3 months ago I reached out to you via email. Would love to chat about tensor-based framework I am working on. Reply Top is selected, so you'll see featured comments

What is a tensor?

What is a tensor? Auto-dubbed ScienceClic Plus 23.5K subscribers Subscribe 5.5K Share Save Clip 191,257 views Feb 15, 2023 Niveau Bac +2 An introductory video to the concept of a "tensor," suitable for upper high school/early university level. The focus of this video isn't so much on the rigorous mathematical details, which may be explored in more depth in other videos, but rather on the intuitive understanding and "true" definition of the concept. 0:00 - Incorrect definitions 4:37 - Review of vectors 9:41 - Definition of a tensor 12:50 - Example: the dot product 16:12 - Coordinate decomposition How this was made Auto-dubbed Audio tracks for some languages were automatically generated. Learn more Chapters View all Explore this course 15 lessons Niveau Bac +2 ScienceClic Plus Course progress 0 of 15 lessons complete Transcript Follow along using the transcript. Show transcript ScienceClic Plus 23.5K subscribers Videos About ScienceClic Twitter Facebook 406 Comments rongmaw lin Add a comment... Pinned by @ScienceClicPlus @ScienceClicPlus 2 years ago (edited) Attention à 9:05 je passe sous le tapis les détails qui définissent un espace vectoriel pour éviter d'alourdir la vidéo, pour ceux qui sont intéressés voici la définition exacte : Un espace vectoriel V défini sur un corps commutatif K, comme ℝ ou ℂ, est : - un ensemble d'éléments (qu'on appelle des vecteurs) - muni d'une addition de vecteurs notée "+" telle que : • l'addition est commutative : u + v = v + u • l'addition est associative : (u + v) + w = u + (v + w) • il existe un vecteur nul noté "0" : v + 0 = v • il existe un opposé à chaque vecteur, noté "- v" : v + (- v) = 0 - et muni d'une multiplication par un nombre "×" qui est : • distributive par rapport aux additions de V et de K : (a + b) × (u + v) = a × u + a × v + b × u + b × v • associative par rapport à la multiplication dans K : (a × b) × u = a × (b × u) • et pour laquelle l'élément neutre de K, "1", est neutre : 1 × u = u 110 Reply 11 replies @HataSem 2 years ago Waouh !! Limpide comme de l'eau de roche...... après un nombre d'heures énorme à chercher la définition...je tombe enfin sur ta vidéo salvatrice !! .....c'est là que tu comprends que beaucoup d'enseignants explique les tenseurs sans les comprendre!! Vidéo d'utilité publique ! Merci mille fois 29 Reply @charmantolaff9576 2 years ago je savais pas que cette chaine annexe existait depuis si longtemps. SVP faite de la pub les gars. 14 Reply @philippebehe448 1 year ago La différence que peut faire un vrai pédagogue est presque effrayante. Quand il se fait tard dans la vie, quand on pense à tout ce temps perdu et au mépris de soi que l'incompréhension a lentement distillé. Balayé en 24min .Merci 29 Reply 1 reply @jcfos6294 2 years ago Eeeennnnffffffiinnnn!!!!!!! Voila 4 ans que je la réclame cette vidéo !!! 4 ans !!!! Tout vient à point à qui sait attendre !!! En français, et sur les tenseurs !!! Géniale. Merciiiiiiiiii 12 Reply @jmoliner0811 2 years ago En primer lugar, les pido disculpas por no tener un dominio del idioma francés suficiente como para escribir este texto en su idioma. Han tenido Ustedes la rara habilidad de unir el rigor, la pedagogía, la claridad y la integridad científica en una breve exposición de apenas veinte minutos. He seguido multitud de videos, cursos on line y hasta textos dedicados a los tensores sin que ninguno de ellos me diera un concepto claro del mismo. Ustedes lo han conseguido en un espacio de tiempo increíblemente corto. No hacen perder el tiempo en exposiciones absurdas sobre notación ni abordan el tema mediante aplicaciones prácticas que embrollan más que aclarar. Gracias, mil gracias, por su depurada técnica que exponen al conocimiento público por mero altruismo. 30 Reply @misnik1986 2 years ago Franchement, je suis en ma 5eme annee de doctorat en mecanique des fluides, et c'est la premiere fois que je me rend compte que la definition de tenseur comme tu nous a prevenu au debut est fausse. Merci beaucoup pour cette video tres instructive 11 Reply @babacarndoye2281 2 years ago C’est la définition la plus claire que j’ai jamais eut d’un tenseur. Elle est digne de la méthode Feynman. Merci 😊 13 Reply @Sarcaskitten 2 years ago C'est quelqu'un qui bouge en rydhme 118 Reply 3 replies @crequerherve3061 2 years ago Bravo pour votre pédagogie! Il y a 40 ans de cela en prépa , je pratiquais le calcul tensoriel sans avoir aucune notion intuitive sur la nature des tenseurs . Une petite suggestion : une prochaine vidéo sur les coordonnées contra/co variantes , sur les espaces duals/tangent et sur les dérivées covariantes pourrait aider pas mal d’élèves pour qui ces notions restent flou ou disons plutôt non intuitives malgré les « exercices de bases » qu’ils descendent de façons purement calculatoire…..En tout cas Merci! 83 Reply 1 reply @lelfet3177 2 months ago Un petit signe dans chaque formule mathématique, le 🟰 1 Reply @hevinjp 2 months ago C'est beau, c'est propre, belle explication des tenseurs 😎👍 1 Reply @regisvoiclair 3 months ago (edited) Des explications remarquablement claires, merci ! Je relaie. 1 Reply @yusufhildevert1749 1 year ago Excellent point de vue ...un tenseur est une application multilinéaire et puis c'est tout. 3 Reply 2 years ago J’adore cette vidéo. Vraiment très claire pour démystifier les tenseurs. 8 Reply ScienceClic Plus · 1 reply @georgesiyombe5195 2 years ago Cette superbe vidéo laisse un goût d'inachevé 3 Reply @xelopeur 2 years ago tu lis dans mes pensées, j'étais à la recherche de cette vidéo précisément et c'est toi qui la sort, magique 4 Reply @ayefounegautiersomane2592 2 months ago (edited) Merci pour votre vidéo. Elle est claire et définie bien un tenseur au sens géométrique. Elle permet également de mieux comprendre ce qu'est un tenseur. 1 Reply @bluelagoon9779 2 years ago Enfin une explication claire de ce qu'est un tenseur ! 6 Reply @Philippe-u4r 11 months ago 1 pour 1000 de la population francophone a vu votre vidéo sur les tenseurs !!! 1 Reply @Camille-wr6vh 10 months ago Très bonne vidéo ! C'était très instructif et claire ! 2 Reply @lemniskate_ayd 2 years ago Quelle limpidité légendaire ! Mercii ! 3 Reply @julesdumont5527 2 years ago waouw merci pour ça ça fait 1 an je cherche à comprendre la subtilité des tenseurs et leur représentation et ta vidéo est parfaite 3 Reply @hugoreytinas5170 2 months ago Félicitations !!! Pour la première fois une explication claire sur ce qu'est un tenseur... 😊 1 Reply @Arcturus1212 4 months ago Merci beaucoup pour cette explication simple et claire. Bravo 1 Reply @ubyrower2043 11 months ago ça donne tellement envie d'applaudir ! 2 Reply @dragweb7725 2 years ago Merci d'avoir démystifié cette notion, je suis étudiant en Mécanique Quantique et je n'avais toujours pas vraiment compris la différence entre tenseur et matrice, en mettant la notion sous le tapis tant que j'en avais pas trop besoin pour avancer. Maintenant c'est bcp plus clair et du coup plus abordable, donc merci 5 Reply @johnmichel7061 2 years ago le don d'expliquer les choses. Bravo. 2 Reply @keetvinyt 2 years ago (edited) On attend une vidéo sur ta chaîne principale ! 3 Reply @titimom5906 11 months ago Merci pour ce travail de fond, 1 Reply @TheSqdqd 2 months ago Merci pour cette vidéo de vulgarisation qui permet d'apres les commentaires d'éclairer cette notion. Trois remarques : 1) tu dis que le produit scalaire dans sa définition analytique au lycée (xx' + yy') est fausse car elle depend des coordonnées et donc du repère choisi...... C est vrai et faux ! On dit bien au lycée que pour tout repère orthonormé ( donc angle droit + norme 1) le produit scalaire (xx' + yy') n'est pas modifié ! Le résultat est donc bien le même ... Mais les élèves ne retiennent que la formule (qui est sécurisante). Il est faux de dire que cette définition n est donc pas bonne...et d'ailleurs tu en fais la preuve à la fin. Il suffit de remplacer tenseur par produit scalaire (forme bilineiare anti symétrique positive).... Et tu montres bien que ca ne dépend pas du repère RON choisi ! 2) la matrice que tu montres à la fin est tout simplement une matrice de passage. AUTREMENT DIT, Si le nouveau repère n'est pas orthonormé, on se demande comment est modifié exemple les coordonnées d'un vecteur, la matrice représentabt une application linéaire, le produit scalaire ou les tenseurs. Et comme c'est llnéaire, il suffit de connaître dans notre cas 4 nombres (Tx,x Etc ) ...bref en remplaçant tenseur par application linéaire, ta démonstration ne changerait pas... 3) dire qu'un vecteur est une fleche peut aussi nuire à la bonne compréhension. On peut dire qu'un espace vectoriel est un ensemble contenant des objets qui est régi par des règles (que tu décris). C'est abstrait. Et donc une fonction (qu'on a du mal à voir comme une fleche) est bien un vecteur (dans un espace vectoriel bien défini)... Je voyais tout en fleche quand j'étais étudiant mais c'était très limitant pour les fonctions ou pour les objets qui ne se voient pas en dimension supérieur à 3.... En somme, il me semble qu' une vidéo sur les applications linéaires (il suffirait de remplacer T partout) permettait de mieux comprendre. Et finalement on pourrait dire que les tenseurs son un cas particulier. Cdt, 2 Reply @mhammedaneb4635 2 years ago Salam Professeur Merci beaucoup, c est extraordinairement bien expliqué, Ça fait longtemps que j entends parler des tenseurs et c est la 1ère fois que je sais ce que c est comme éléments mathématiques Merci 3 Reply @lavoixnordsud7471 4 months ago Bien présenté. Merci 1 Reply @abderrahmanesaihi4732 11 months ago Claire, nette et précise, impeccable. Merci 1000 fois ne suffit pas. 1 Reply @jean-lucgostijanovic3688 2 years ago enfin une vidéo où l'on m'explique l'intérêt des tenseurs bravo à toi 👏 1 Reply @ReveilLunaire 2 months ago Un tenseur c'est un danseur allemand..ahhh ya ya ya ... véridique !! 3 Reply @Also_sprach_Zarathustra. 2 years ago Je n'ai plus fait de maths depuis le lycée, et pourtant tes explications sont limpides comme de l'eau de roche ! C'est vraiment incroyable d'avoir la chance de rencontrer en vidéo quelqu'un d'aussi pédagogue que toi, s'il te plait continue ! 40 Reply 3 replies @jms07000 2 years ago Merci, je commence enfin à comprendre ce qu'est un tenseur, vite la suite ! 2 Reply @franckporcher 2 years ago Magnifique pédagogie, d'une clarté qui illumine les ténèbres. Un grand merci pour cet effort de clarification, et finalement, de simplification. J'ai étudié plusieurs années la physique à Orsay il y a près de 45 ans, et donc pratiqué le calcul tensoriel, et jamais les tenseurs n'étaient présentés comme ici pour ce qu'ils SONT. Et pourtant les profs étaient quasiment tous médaillés...n'est pas Feynman qui veut ! BRAVO ! 3 Reply @mathemaxime 2 years ago Merci pour cette vidéo ! L’effort de vulgarisation est très appréciable pour un élève de sup un peu curieux 🙂 3 Reply @ves7y775 2 years ago Je connaissais la chaine principale mais pas la secondaire et justement en voyant les vidéos sur la principale je me disais toujours qu’il manquait d’explications mathématiques, alors très heureux de découvrir cette chaine 5 Reply @lenekogilles7254 2 years ago Merci beaucoup ! J'avais toujours un peu séché sur la notion de tenseur. NEKO 2 Reply @davidniddam9869 1 year ago Excellent, step by step partant des bases 👍 1 Reply @tiemogoolivieryahiry6080 2 years ago Trop clair dans mon esprit 1 Reply @Promeneur 2 years ago Merci ! Et bravo pour votre clarté. 3 Reply @anobi2 2 years ago Un must watch pour une intro en algèbre bilinéaire. Tout va tellement plus vite dans l'esprit quand on a la bonne intuition, merci ! Reply @tfrank2695 1 year ago Mais c'est le précepteur qui gère cette chaine !!! Il a exactement la même voix Reply @gerardzi7930 2 years ago Introduction de ce concept par l'algèbre des formes linéaires est plus facile mais l'explication reste intuitive et facile à comprendre ! Un livre chez l'éditeur Ellipses , très bien pour l'étude des tenseurs : Titre Initiation progressive au calcul tensoriel 158p de Claude JEANPERRIN 1999face-blue-smiling 4 Reply @remidebard7431 2 years ago Merci beaucoup. Je faisais la confusion entre matrice et tenseur. Je comprends maintenant qu'un tenseur existe indépendamment d'une matrice et qu'on peut avoir une matrice de tenseurs. C'est beaucoup plus clair maintenant. 3 Reply ScienceClic Plus · 1 reply @ptyxs 4 months ago Passionnant. 1 Reply @Pierreloutonbleu 2 years ago Merci pour cette vidéo ! L'explication est clair et les dessins sont parlant, vraiment parfait ! 3 Reply @mackey4462 1 year ago Explications brillantes ! Merci beaucoup ! 2 Reply @Anna801 2 years ago Merci infiniment. Pour la première fois je trouve une explication concrète du mot tenseur. 1 Reply @francoisbaugey2570 2 years ago Super intéressant... L'illustration avec le produit scalaire est parlante... Bravo 2 Reply @mathematrice 2 years ago Cette vidéo tombe à pic, merci ! 2 Reply @jeremiedelusignan950 2 years ago Super heureux de voir une nouvelle vidéo de ta part, et sur un sujet très intéressant en plus ! 5 Reply @joelbecane1869 2 years ago C'est la première fois que j'arrive à comprendre ce qu'est un tenseur, merci beaucoup :) 4 Reply 1 reply @eliottd6470 1 year ago Merci beaucoup pour ces précisions très claires 1 Reply @jean-louismartin8875 2 years ago Merci, c'est formidablement bien fait! 2 Reply @charmantolaff9576 2 years ago (edited) Quand je vois science clic, je m'abonne d'abord tellement je suis convaincu que ça sera de qualité. 1 Reply @paulfrancoisantoine5752 2 years ago Encore une super vidéo comme toujours v est super bien expliquer,conscis et concret 5 Reply @nicholegendrongendro 2 years ago Merveilleux 🕊️🕊️🕊️ 2 Reply @alexandrechellet435 2 years ago Très pédagogique . Merci. 2 Reply @moonyoff 2 years ago Ha enfin une vidéo que je vais comprendre ! 👍 Continues comme ça ! 2 Reply @clauded3220 2 years ago Bravo pour votre pédagogie. Limpide ! 2 Reply @ytbelo 1 year ago Enfin, je sais ce qu'est un tenseur. Merci ! Elémentaire mon cher Watson. Reply @sousounounou05 2 years ago Merci, Très didactique 2 Reply @baptistebauer99 2 years ago Super petite explication!! Merci beaucoup :) 2 Reply @lyrdsngc3210 2 years ago Merci pour cette explication. 2 Reply @ChristBeloved-17 2 years ago Merci pour cette vidéo. Je l'ai beaucoup aimé. Peux tu nous faire des vidéos sur d'autres tenseurs comme le tenseur de Riemann ou encore le tenseur de Ricci . Merci 3 Reply @florianmarie-celine4571 1 year ago Je trouve vos explications d'une grande qualité ! Vous parlez de manière fluide et agréable à mon sens en prenant soin d'utiliser tantôt des mots simples, tantôt un langage technique. Les schémas en couleur sont aussi particulièrement bien pour se représenter intuitivement/visuellement le concept. Vous rendez cette notion accessible au jeune lycéen que je suis, merci. ❤ 1 Reply @mohamedhamadene8522 2 years ago Merci pour la simplicité, l'explication est extra merci encore 1 Reply @davidniddam9869 2 years ago (edited) Merci pour votre Clarté qui nous poussent à vous écouter avec encore plus d’attention. Il faudrait une vidéo sur les changements de base et pkoi changer de base… et le déterminant après changement de base 3 Reply @stephaneg.8142 2 years ago Merci beaucoup c'est très intéressant et très clair. Je ne connaissais pas le principe du tenseur et votre explication est très clair. Vivement la suite ! 2 Reply @zak9X 2 years ago Merci beaucoup pour cette vidéo, c'est très clair. 2 Reply @patricelheritier3112 2 years ago Il y a dès le départ des inexactitudes dans ces définitions, par exemple, un vecteur n'est pas une flèche mais une classe d'équivalence qui pour chacune d'elles correspond géométriquement à une direction, un sens dans cette direction et une "longueur" ( son module) et peut donc se représenter par des flèches (en dimension 2 ou 3) d'autre part le produit vecteur par un réel n'est pas une propriété, mais une opération (application de l'ensemble produit vecteur réel dans l'ensemble des réels)... 1 Reply @daoudatakoubakoye5115 9 months ago Oh là quelle simplicité? Terrible! vraiment vous étiez où tout ce temps? On a galéré en classe de physique Reply @felixbouvet1746 9 months ago Merci beaucoup d'avoir expliqué les produits produit scalaire et les équations du vecteur de l'espace ça m'a permis de rafraîchir un peu la tête vous vous expliquez bien Reply @jean-christophelelann6308 2 years ago Best definition ever ! 2 Reply @TheTruth181818 2 years ago Incroyable de clarté et de pédagogie. Merci. A noter que la notion de tenseurs en machine learning n'a pas grand chose à voir avec la "vraie" notion mathématique présentée ici, mais correspond plutôt à la version dégradée décrite en début de vidéo. 1 Reply @oxidiezed 2 years ago Vraiment tu as ce don pour rendre les trucs les plus barbans de la fac intéressants et ca me donne presque l'envie de finir ma licence de maths 4 Reply 1 reply @joluju2375 6 months ago Très agréable, je ne peux comprendre qu'en ressentant les choses, et là ça m'a un peu aidé. J'aimerais savoir comment le mot "tenseur" a été choisi, et en particulier si ça peut avoir un rapport avec tension ou déformation d'un truc élastique, ou si ça n'a aucun rapport. La question n'est pas innocente, si on accorde de l'importance à l'aspect géométrique, on peut supposer qu'il y a quelque part un rapport avec le monde réel. 1 Reply @Thomas-tz9qv 2 years ago Excellente video de vulgarisation (tout en poussant le bouchon un peu plus loin que d'habitude), tu as un abonné de plus. En attendant des prochaines création ;-) 2 Reply @oga657 2 years ago Pas mal , je m'abonne 😉👍😂 2 Reply @wernerlippert5499 2 years ago Excellent! 2 Reply @faycelhennous8359 2 years ago Super vidéo, pourrais tu faire une vidéo sur les TORSEURS utilisés en mécanique du solide ? PS : Youtube ne me recommande que très peu tes vidéos alors que tu en as sortis beaucoup. Grand merci en tout cas. 6 Reply @jop9436 2 years ago quoi dire ... génial ! 1 Reply @jardozouille1677 2 years ago (edited) Hum ... super intéressant. Il nous faudrait une suite : comment est-ce qu'on multiplie les matrices qui représentent des tenseurs ? 2 Reply @zahialaouid3989 2 years ago Bravo ! 2 Reply @KarimOunnas-y2l 2 years ago Merci , super bien expliqué. 1 Reply @kwaichangcaine7347 2 years ago Merci pour cette excellente vidéo... 👍 Vous serait-il possible de faire une vidéo sur les équations de Maxwell ? On ne trouve rien de satisfaisant sur le net...merci pour votre retour... 2 Reply @alain1312 2 years ago Super clair. Merci 2 Reply @lastday3439 10 months ago (edited) Il me semble que cette définition ne marche qu’en dimension finie, où le produit tensoriel d’espaces vectoriels coïncide avec les formes multilinéaires, ce qui n’est plus le cas en dimension infinie. Une définition d’un tenseur serait tout "simplement" qu’il s’agit d’un élément d’un produit tensoriel d’espaces vectoriels voire plus généralement de modules. 2 Reply @thanhquannguyen9624 1 year ago Merci. J'ai beaucoup apprécié ce video sur les tenseurs. Y a-t-il une suite à ce video ? 1 Reply @SefJen 2 years ago Je viens de découvrir cette nouvelle chaîne (SC Plus), j'ai adoré. As-tu prévu de faire une suite pour expliquer le calcul tensoriel en maths, et en physique ? 4 Reply @marinacb73 2 years ago Merci beaucoup!! 2 Reply @mohsentroudi9568 3 months ago Mille mercis ❤ Reply @philippelobello4288 2 years ago Félicitations pour la clarté des explications ! Si mon prof de physique (en licence, il y une quarantaine d'années :)) avait abordé les tenseurs de cette manière, j'aurais compris de quoi il s'agissait... C'est aujourd'hui chose faite ! Un grand merci !😀 4 Reply 1 reply @zazavitch1 2 years ago Merci très intéressant 2 Reply @vitormirandinha 2 years ago Merci beaucoup! Três didactique 2 Reply @Palu-eu8tj 2 months ago Tenseur de contrainte en mécanique 1 Reply @livensonchery281 1 year ago J'utilise les tenseurs tout le temps et j'avais rien pigé du tout. Merci 💯🚶🏾‍♂️ Reply @jeromelarose4886 2 years ago Bravo et merci pour cette pédagogie incroyable. Bonne continuation. 1 Reply @riadhkhlif7059 2 years ago Bonjour, vos vidéos sont absolument incroyables, de très grande qualité et rigueur. Je crois pouvoir réussir mon bachelor en physique théorique avec vos vidéos. Quelle est la fréquence d'apparition de vos vidéos? Croyez-vous poiuvoir faire une par semaine? 3 Reply @izaret 2 years ago Bravo, tres bien expliqué. La meilleure vidéo en Français a mon avis sur le sujet qui est, en général, très mal enseigné en prépa et même en école d’ ingénieur. La prochaine vidéo introduira les complications de l’espace vectoriel dual? La série vidéo d’eigenchris en anglais est elle aussi excellente. 2 Reply @norbertdelorme8892 6 months ago Génial ! Merci ! Reply @Jipeash 2 years ago En 3:24 vous passez d'un tenseur T "qui serait une sorte de matrice avec des nombres" à "si on change de coordonnées pour décrire notre espace" sans transition... 1 Reply @ТоварищСталин-и1ц 2 years ago (edited) Finalement, un vecteur est un tenseur, un tenseur est un vecteur... 🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔 Super vidéo camarade 1 Reply @fabienleguen 2 years ago Merci c’est limpide et c’est esthétiquement agréable à regarder ! En prépa (ça remonte…), j’avais compris cette caractéristique fondamentalement géométrique des tenseurs mais en revanche, il y avait deux objets que je manipulais mécaniquement sans vraiment comprendre leur nature profonde : le produit tensoriel d’espaces et le produit tensoriel d’applications linéaires. Ces objets ont-ils une nature géométrique ? S’ils sont nommés ainsi, Il y a forcément une connexion avec les tenseurs non ? Si oui, j’adorerai une vidéo de suite à celle-ci ! Merci pour ton travail 4 Reply @hikari9629 2 years ago Super clair merci beaucoup ! 2 Reply @gilldeguill 2 years ago Intéressant mais du coup ce serait bien d’avoir une suite qui explique pourquoi les tenseurs ont été utilisés en relativité surtout générale. Je me demande aussi pourquoi (a ma connaissance) on ne les utilise pas dans le formalisme quantique 2 Reply @WahranRai 2 years ago Si vous utilisez la terminologie des espaces vectoriels (vecteurs, scalaires ...) , je préfère dire scalaire à la place de nombre : multiplier par un scalaire 1 Reply @hassantahri973 1 year ago Le vecteur v n’est pas obligé de passer par zéro.C’est la derction qui est importante . Mais le vecteur peut être ailleurs très loin de l’origine D’ailleurs c’est comme ça qu’on definit deux droites parallèles elles ont le même vecteur directeur. Ainsi deux droites parallèles peuvent très espacées 1 Reply @SamuelNgoye 2 years ago Bonjour je vous remercie infiniment merci 1 Reply @juancarlossanchezveana1812 1 year ago Amazing 1 Reply @petrkisselev5085 2 years ago Superbe vidéo ! Je n'avais jamais vu les tenseurs sous cet angle, et pourtant j'en ai vu des soi-disant tenseurs au cours de ma formation universitaire. Ta présentation a aussi répondu à une question que j'avais depuis longtemps en tête à propos de la différence entre tenseurs et matrices. Mais je pense que cette vidéo mérite une suite, car les tenseurs tels que présentés ailleurs utilisent des vecteurs qui peuvent être covariants ou contravariants (lequel des deux est analogue aux formes linéaires déjà 😅). Le sujet mérite d'être discuté avec la même limpidité que la définition de base présentée ici. Reply @laurent-ym2jw 11 months ago bref tenseur : formes n-linéaires sur un produit d'espaces vectoriels ? 1 Reply @adrienrivas5531 2 years ago 👍👌👏 4 Reply @cherbiammar3527 2 years ago Bonjour Monsieur J'ai suivi avec un grand intérêt votre cartouche traitant d'introduction du concept de tenseur. c'est tellement très intuitif et bien séquencée que j'ai vu et revue votre vidéo à maintes reprises et comme ça me laisse sur ma faim j'ai décidé de vous écrire et ce, dans l'espoir que vous nous présentiez cet objet si abstrait dans le cas général . en effet, à 12.46 vous définissez le tenseur comme une application bilinéaire de EXE------------------- IR et dans l'exemple d'application vous avez privilégiez un repère orthonormé avec seulement les coordonnées contra variantes. c'est vraiment très imagé et intuitif comme introduction . Cependant , dans le cas général le tenseur est défini comme une application multilinéaire de E x E...X E*.......----------------------- IR Ainsi je vous demande de nous éclairer , dans la mesure du possible, sur l'ensemble de départ de cette application qui associé en même temps les espaces vectoriels ( Vecteurs) et les espaces duaux ( formes linéaires, qui sont elles mêmes des applications linéaires de E---------------- IR). Et pour l'application nous souhaitons un exemple ou il sera traité des deux types de composantes ( Contra variantes et covariantes) dans un repère quelconque et ce , pour aboutir à la base des espaces tensoriels qui est le produit tensoriels des vecteurs de base Je vous remercie infiniment pour ce que vous faite et bon courage à vous Reply @SoftYoda 2 years ago Il me faudrait la même vidéo avec un alphabet non grec, ou alors avec des couleur pour chaque lettres que je connais pas, pour faire de la synesthésie. 4 Reply 1 reply @jeanluczieten544 2 years ago excellent 1 Reply @kunaiJR 2 years ago 7:14 Merci pour la clarification. Pour moi la géométrie ca a toujours été de l'algèbre en définissant une origine alors que dans ma tête sa servait à rien puisqu'on peut se ramener à de l'algèbre. 1 Reply @franckporcher 2 years ago @Polymath Freeman, merci de publier ton CV, introuvable sur ta chaine youtube. Reply @Qubot 5 months ago Un tenseur est une relation entre plusieurs vecteurs. 1 Reply @quannguyenthanh8868 8 months ago Merci beaucoup. Reply @libregisin9878 2 years ago Merci pour vos explications très claires. Maintenant, j'aimerais savoir la différence entre des tenseurs covariants et contravariants. 3 Reply 1 reply @Also_sprach_Zarathustra. 2 years ago Aussi, as-tu penser à collaborer avec l'éducation nationale (ou autre) pour proposer tes services aux plus grands nombre avec plus de moyens ? (Vraiment tu es un pépite, j'espère qu'on ne te laisse pas te dé-patauger tout seul) 1 Reply @CrazyShores 11 months ago Très bien mais une précision. Un tenseur et une forme MULTILINEAIRE, pas seulement linéaire. 1 Reply @bbbenj 2 years ago Ça semble touffu mais en fait non. Je n'ai pas mis les mains dedans depuis 30 ans mais j'ai à peu près compris ! 1 Reply @jcfos6294 2 years ago En réalité, rien en mathématiques n'est compliqué. Non, rien. Tout dépend, de comment on vous enseigne les choses. Plus la personne qui vous enseigne, est à l'aise et maîtrise son sujet jusqu'à le rendre passionnant et fluide, p'us vous même vous apprenez "comme dans du beurre"! Quand ça coule de source, alors réellement, n'importe qui est capable de comprendre et d'acquérir des compétences développées, spécialement en mathématiques. Vive les mathématiques, vive la science physique, vive la théologie (la science des sciences, celle qui tend à développer toute votre intériorité, votre development personnel) 3 Reply 2 replies @Louis-ml1zr 2 years ago Merci pour la clarté des explications ! Auriez vous un bon livre anglophone ou français permettant d’aller plus loin mais aussi d’introduire les différents concepts du calcul tensoriel ? 2 Reply @bambino3455 2 years ago (edited) Les tenseurs sont définie si je me souvient bien comme une forme linéaire sur le produit tensoriel de k copie d'un espace vectoriel et de l copie de son dual ! Comme une application bilineaire sur E×F s'identifie à une unique application linéaire sur leur produit tensoriel. Est ce qu'il en va de même pour les application multilinéaire ? Et donc définir un tenseur comme une application multineaire sur E^k×(E*)^l est identique à celui d'une application linéaire sur le produit tensoriel associé. Merci. 3 Reply @andreguillaume79 2 months ago Et à quoi ça sert ? Je ne demande pas ça méchamment, j'aimerais savoir. Cordialement. 1 Reply @rolandfaucon1560 1 year ago (edited) J'ai cru que tu y arriverais pas! accélère Alex!!🤣🤣🤔😛🤧 Reply @Timi07 2 years ago J’ai rigolé 😂😂tellement que ça dégage le flou dans ma tête. Donc j’allais enseigner aux enfants un vecteur n’existerais jamais sans espaces ( ou repères) . Mdr , merci beaucoup ☺️ Reply @Charles25192 2 years ago Fin de lycée ? J'ai fait une terminale scientifique il y a 30 ans et on n'avait même pas vu les matrices. 1 Reply @MrYellowm4n 2 years ago Merci beaucoup la premiere definition de tenseur comprehensible je connais .J'ai l'ai demandé à mainte fois à des agregé ....ils ne pouvaient pas me dire concrètement ce qu'etait un tenseur .c'est l'objet mathématique qui rend incompréhensible les equations d'einstein Reply @ahmatmalloum9837 2 years ago Merci pour la video, cependant la définition de l'espace vectorielle est ambiguë, il faut juste ajouter que les opérations multiplication par une constante, additions entres les éléments fournissent des nouveaux éléments appartenant à cet espace vectoriel...en gros comprendre que votre "il existe" signifie appartient à l'espace vectoriel considéré. 1 Reply @llury31415 1 year ago (edited) Un tenseur n'est qu'une forme multilinéaire ? Moi qui croyait que c'était un tout autre objet compliqué... Merci pour cet éclaircissement. Reply @thanhquannguyen9624 2 years ago Merci. 1 Reply @MamadouAlphaDIALLO-uq2uv 1 year ago Je retiens qu'un tenseur, comme un produit, EST une opération qui prend en entrée des vecteurs et qui revoit un réel 1 Reply @uranium-h3o 3 months ago Donc T(u, v) = u^t Av où A est la représentation matricielle du tenseur (dans le cas du produit scalaire A = I). C dingue que n'importe quel tenseur d'ordre 2 peut être vu comme un produit scalaire entre un vecteur et une transformation linéaire d'un autre vecteur. 1 Reply @monsieur3dx 2 years ago "Ce qui se conçoit bien s'énonce clairement, et les mots pour le dire arrivent aisément". Avec ici une grès grande sobriété, tant dans la forme que dans le fond. Pourrais-je connaître votre application de tableau interactive ? Tablette graphique avec écran ? Peut-on de dessiner ainsi dans le cadre d'une application de visioconférence ? 1 Reply @octobre4623 2 years ago Merci beaucoup. Maintenant quel rapport avec le tenseur des contraintes et le tenseur des déformations qu'on m'a enseigné en résistance des matériaux (et que j'ai fort peu compris) ? 2 Reply @louismercier3051 2 years ago (edited) Merci beaucoup pour cette vidéo, et toutes les autres que je n'ai pas pris la peine de commenter jusqu'à présent 😄 C'est l'explication la plus rigoureuse et la plus compréhensible sur les tenseurs auquelle j'ai eu accès jusqu'à présent! Si je peux me permettre juste une petite remarque, il "manque" la formule final pour calculer le résultat du tenseur appliqué à deux vecteurs à partir de la matrice: "x transpose fois T fois y. Je suis pas sure que ce soit évident pour tout le monde vue que, généralement, on multiplie une matrice à droite par un vecteur colonne pour obtenir un autre vecteur colonne, ici, il faut en plus multiplier aussi à gauche par un vecteur ligne pour au final obtenir un nombre (ou plus généralement un scalaire). Encore bravo pour toutes vos vidéos qui sont formidables 😃 18 Reply ScienceClic Plus · 3 replies @jeanluclemoineable 2 years ago Bonjour Belle chaîne ! Quel outil utilisez vous pour réaliser vos vidéos. C'est comme un tableau. C'est très clair et beau. Merci pour votre réponse. Reply @ggousier 11 months ago Moi si j'étais vous je changerais le nom de la chaîne, au lieu de "ScienceClic" je la renommerais "Science_Déclic" 🤣. 1 Reply @nicolaslhomme2117 2 years ago Merci 1 Reply @guillaume8672 2 years ago Petit plus a rajouter très important. Un espace vectoriel n’est pas vide, ne pas oublier de mentionner l’existence de l’élément nul ;) 2 Reply ScienceClic Plus · 1 reply @louiseb3146 2 years ago C'est amusant parce que moi, en physique, j'ai toujours utilisé utiliser le mot tenseur comme une généralisation d'un vecteur, sous forme de matrice. Proche de cette première "fausse idée", bien que non, je n'ai jamais considéré que c'était simplement une matrice à 3D. Non, pour moi un tenseur c'est un vecteur d'ordre variable, mais pas une application, en particulier pas un produit scalaire dans un cas particulier. Pour exemple, le plus intuitif c'est pour moi le tenseur de gradient de déformation en mécanique solide. 2 Reply 1 reply @EricBrunoTV 2 years ago Merci pour votre bonne explication. à quoi sert un Tenseur? Quelles limites ont poussé à son utilisation? Quels besoins? Merci!! 1 Reply @lesavdesabonnes 2 years ago 🤔<(Tenseur?!) 🤷‍♂️<(Toi même!) 🤭 1 Reply @et-touriabdelhak4748 2 years ago Merci beaucoup pour cette video, SVP ma question est vous travaillez Mr par quels outils pour faire ce genre de video 1 Reply @celestus69 2 years ago J'aime cette présentation, simple et pédagogique. Mais du coup, si le tenseur est une opération, quelle est son opposé ? (Comme la soustraction est l'opposé de l'addition, la division pour la multiplication, la racine pour la puissance, etc.) 1 Reply @cybersolo 3 months ago Je n'avais jamais entendu parler du concept de tenseur, même dans mes cours d'université (qui datent des années 90). Le produit scalaire y est juste défini comme une somme en fonction des coordonnées. 1 Reply 3 replies @LouisdeGonzagueLissom-zm2hr 1 year ago Merci pour cette vidéo. Je suis très content. Comment faire le produit tensoriel à partir de cette définition ? Reply @jonathanmilon2415 2 years ago Merci pour cette vidéo. Serait-il possible que vous fassiez une vidéo similaire dans laquelle vous expliquez la signification physique et géométrie des tenseurs qui interviennent dans l'équation de la relativité générale d'Einstein ? 2 Reply 1 reply @dionys0s 2 years ago Très intéressant ! Par contre, tu aurais pu mentionner le tenseur de Rodin à 00:23. 4 Reply 1 reply @rlys-lah2731 2 years ago Voilà ! Pourquoi ne nous intéressons nous jamais aux définitions fondamentales des choses ? Par manque de temps ? Je pense que si dès le début on s'intéressait aux fondements les élèves iraient moins vite certes mais descendraient tout après, et on aurait une génération de génie absolue, mais ce n'est que mon avis. Reply @MichelBOUCHARDY-wq9jk 2 months ago Tenseurs et torseurs....., cauchemards des " prépa." ...! 1 Reply @sidiabdelhaksbai6422 2 years ago Dans l espace c est applicable. Dans le temps le tenseur devient un gros volcan Reply @NEO-c5w 2 months ago Ne dites pas tous, Moi je n'ai jamais vu un vecteur au lycée...! 1 Reply @73framzy 3 months ago (edited) 0:27 il y a le tenseur de Rodin aussi 😅 2 Reply 2 replies @xaviermadre1767 2 years ago Mais alors dans ce cas là le produit scalaire usuels en mécanique quantique n'est pas défini comme un tenseur car il est sesquilineaire et donc antilineaire par rapport au premier vecteurs ? 1 Reply @TheyCallMeHacked 2 years ago Je tiens à corriger le fait que les couples de nombres sont bel et biens des vecteurs (du moins dans le sens d'un vecteur en algèbre linéaire) au même titre que les flèches du plan. En algèbre linéaire, on définit même le (ou un) plan comme n'importe quel espace vectoriel à deux dimensions, cela inclue donc aussi l'espace ℝ² des couples de réels, mais aussi par exemple l'espace ℝ₁[X] des polynômes à coefficients réels de degré inférieur ou égal à 1 2 Reply ScienceClic Plus · 5 replies @xavierflaminus7277 2 years ago J'avais appris en mécanique en principe fondamental de la statique le TORSEUR d'action mécanique ou l'on fesait le produit scalaire d'un TORSEUR avec des vecteurs forces dans la première colonnes et le vecteur moment en deuxième colonnes et on déplacé cette force a un autre point pour savoir quel force et couple est appliqué à un autre point pour déterminer le Résistance Des Materiaux. Mais je me rappel que l'on fesait un calculé z=x1*y2-y1*x2 Je n'ai jamais retrouvé ce produit scalaire dans l'espace? Reply @alkacil2504 1 year ago Pour comprendre ce qu'est un tenseur, consultez un cours d'algèbre multilinéaire ! Reply @dark-bubble-learning 2 years ago (edited) Merci pour cette très intéressante vidéo ! Penses-tu faire une vidéo de ce genre sur l'espace dual et le concept de variance ? 3 Reply ScienceClic Plus · 2 replies @dremaro2967 2 years ago (edited) Ho, en voilà une vidéo qu'elle est utile ! on vient justement de finir les cours de MMC solide (prems hehe) 2 Reply 5 replies @davidyama7396 2 years ago 😊 1 Reply @pierremihalic9178 2 years ago Bonjour, avec cette présentation comment vous montrez q un vecteur est un tenseur ? 1 Reply @laurentsemard8351 2 years ago CQFD.... 👏🏻👏🏻👏🏻 Reply @ArcturiusX 2 years ago Faut-il absolument qu'un tenseur soit un réel ? Un champ de vecteurs (R^d dans R^d) n'est il pas un exemple de tenseur ? 1 Reply @Maxence1402a 2 years ago Dans la définition d'un tenseur, j'ai l'impression que tu définis plutôt une forme multi-linéaire. Il me semble que l'image d'un tenseur peut être un vecteur, une forme linéaire ou plus généralement un tenseur ^^ 2 Reply ScienceClic Plus · 1 reply @daniellippert540 2 years ago Merci maître ! Juste un détail hors propos (mais a son importance): pourquoi les nombres linéaires infiniment précis ("lips")sont-ils appelés des nombres "réels" ? Reply @sidiabdelhaksbai6422 2 years ago Comme le vecteur facteur des postes Reply @etsugua4599 2 years ago 12:00 à ce stade j'ai envie de dire que c'est une application bilinéaire de E² dans R où E est un espace vectoriel, c'est bien ça ? 2 Reply ScienceClic Plus · 1 reply @bouyaka7863 2 years ago un tenseur d'ordre n n'est rien de plus qu'une forme n-linéaire O_O 1 Reply @yannld9524 2 years ago C'est marrant cette description des vecteurs qui est faite : vous les définissez algébriquement mais vous persistez à leur donner une interprétation géométrique. C'est en effet le point de vu historique et c'est pas faux non plus mais cela nécessite de se donner une base et donc de faire un choix. Essayer systématiquement d'interpréter géométriquement les vecteurs peut parfois nous coincer, notamment en grande dimension ou quand on se place sur un corps (ou même un anneau) un peu plus bizarre que R. Aujourd'hui les mathématiciens se sont rendus compte qu'on peut faire plein d'autres choses que de la géométrie avec les vecteurs, et en plus la définition algébrique est quand même beaucoup plus élémentaire à mon humble avis. Bon évidemment je chipote la vidéo reste de bonne qualité. 2 Reply ScienceClic Plus · 4 replies @brice-mb 1 year ago (edited) Je découvre les tenseurs et je trouve que cette vidéo est excellente👏🏾. En revanche je me pose les questions suivantes: - La transformation d’un tenseur sur des vecteurs engendre toujours un scalaire ? - Est-il possible d’avoir une application bijective ou surjective ou injective ? Genre tu peux passer d’un scalaire à un tenseur (à sa représentation abstraite) ? Merci par avance pour vos éclaircissements 1 Reply 1 reply @saidagouar5119 2 years ago Merci pour votre éclaircissement de point vue rationalité mathématique logique ,mais la formulation de l'équation de la relativité générale est physique ,elle signifie quelque chose d'energitique phénomènale objectif qui appartient aux processus de la sensibilité et de l'intuition humaine ,c'est a dire à l'essence de l'esprit humain qui comprend et prend conscience des phénomènes réelles emperique qu'on peut vérifier expérimentalement et non mathématique sec qui ne sert que de la symbolique rationnelle pour quantifier ..... Reply @brahimsorroche4075 2 years ago (edited) Travail : action - réaction = Temps Reply @amoumhamid8087 1 year ago Il ya aussi la notion de TORSEUR qu'elle est complètement différente de celle de TENSEUR. Reply @justchill4297 2 years ago Les tenseurs sont des matrices 5 Reply ScienceClic Plus · 1 reply @hassantahri973 1 year ago Autrement dit un tenseur peut être complètement déterminer si on le connaît sur la base de l’espace vectoriel de dimension finie bien sûr ça va de soit Reply @Morgatte 3 months ago Si le tenseur (qui est indépendant de toute base) renvoie un scalaire, alors comment se fond les calculs dans une base non orthonormée ? T(ex, ey) qui valait 0 vaut quoi ? comment on détermine-t-on les nouvelles valeurs de la matrice T ? Reply @hokkaido8022 1 year ago C'est pour ça que les fruits et les légumes sont hypertensés Reply @Matt-yv3zn 2 years ago Super vidéo ! Surtout que c'est un sujet complexe :) J'ai l'impression que pour le bien de la vidéo tu as fait une correspondance directe (ou un amalgame) entre tenseur et forme multilinéaire : les propriétés énoncées à 9:41 sont celles des formes multilinéaires. Or les tenseurs peuvent être défini pour le cas plus général des applications multilinéaires. Pour moi, de 9:41 à 22:19 ça aurait été plus général de parler de forme multilinéaire, puis de parler de tenseur car là tu fait allusion au tenseur (aux nombres précalculés pour les vecteurs e_x et e_y). Enfin, je ne sais pas si cela est pertinent, pour la vidéo, de faire la distinction entre la forme multilinéaire et l'une de ses représentations en tenseur. Ce qui me trouble le plus c'est que, pour moi, les tenseurs peuvent être défini comme représentation sous la forme d'un "tabloid de nombre" d'une application multilinéaire. Analogiquement aux matrices, qui sont une représentation sous la forme d'un "tableau de nombre" d'une application linéaire. Et c'est cette analogie que tu adresse a 0:00 et qui est souvent mal expliqué / comprise. Par exemple, pour construire un tenseur d'une application multilinéaire L : E x F x G -> H avec E, F, G et H des espaces vectoriels : - on prends une base de E les vecteurs (e_i), une base de F les vecteurs (f_j), une base de G les vecteurs (g_k) et une base de H les vecteurs (h_p) - pour toutes les combinaisons possibles des (e_i, f_j, g_k) : - on fait la décomposition de L(e_i, f_j, g_k) dans la base (h_p) de H i.e. L(e_i, f_j, g_k) = T_(i, j, k, 1) x h_1 + T_(i, j, k, 2) x h_2 + .... + T_(i, j, k, p) x h_p + .... T_(i, j, k, n) x h_n avec T_(i, j, k, 1), T_(i, j, k, 2), .... , T_(i, j, k, p), .... , T_(i, j, k, n) des nombres alors T = (T_(i, j, k, p)), pour toutes les combinaisons de (i, j, k, p) possibles, est la représentation en tenseur de l'application multiliénaire L dans les bases (e_i), (f_j), (g_k) et (h_p) i.e. "T = tenseur(L, (e_i), (f_j), (g_k), (h_p))" 1 Reply ScienceClic Plus · 1 reply @NohamLebreton 3 months ago 9:31 Il manque aussi le fait que l'espace vectoriel doit contenir le vecteur nul mais sinon c'est bon 1 Reply 1 reply @flew6176 1 year ago Alors un tenseur est-il simplement une forme linéaire dans le sens des applications linéaires ? Reply @rvtirefort 1 year ago Le tenseur de Rodin est pas mal non plus Reply @lucaolmastroni6270 2 years ago (edited) Très belle et très instructive vidéo qui se démarque de beaucoup d'autres vidéos de divulgation sur l'argument des tenseurs. En tant qur de néophyte j'aurais quelque question sur le fait que les tenseurs sont indépendants d'un repère pour la caractérisation des vecteurs qu'ils considèrent: a) les tenseurs font abstraction des référentiels dans lesquels sont exprimées les coordonnées des vecteurs, mais il faut néanmoins fixer à priori, come base, une unité de mesure pour l'évaluation des normes des vecteurs ? Donc en quelque sorte, un repère quelconque est nécessaire ? b) Dans le cas du "tenseur produit scalaire" dans un repère non orthonormé, ni orthogonal, l'évaluation du nombre scalaire résultat doit passer par les transformations de changement de repère, ramennant les composantes des vecteurs à un repère orthonormé, je suppose ? Est-ce bien ce que vous entendez exprimer à la minute 16' ? Merci 1 Reply 1 reply @jean-pierremessager4366 2 years ago Belle vidéo ! Bravo ! Au fait, vous avez vu que Jean-Pierre Petit vous traite d'olibrius quand on lui pose des questions gênantes lors de sa "conférence" du 14 janvier ? 1 Reply 1 reply @ben17012 2 years ago Et du coup la différence entre un tenseur et une "application linéaire", c'est quoi ? j'ai toujours entendu parler du fait qu'une matrice était une représentation sous forme de tableau d'une application linéaire.. 1 Reply ScienceClic Plus · 1 reply @nicolasmenotti 2 years ago Non au lycée nous voyons plusieurs définitions équivalentes du produit scalaire et pas seulement celle avec les coordonnées. 1 Reply ScienceClic Plus · 2 replies @Miawpioupiou 1 year ago Je ne comprend pas, un tenseur renvois forcément un nombre ? En physique, les tenseurs représentent généralement des variations dans l'espace et sonc sont sous forme se matrice ? Reply @nathanmanzambi6950 1 year ago Tout à fait ! Un tenseur ne représente pas nécessairement une application linéaire. Un tenseur est une généralisation d'un scalaire, d'un vecteur ou d'une matrice. Il peut être utilisé pour représenter des quantités physiques comme la force, le champ électrique ou le champ gravitationnel. Un tenseur peut avoir un nombre quelconque d'indices, contrairement à une matrice qui n'en a que deux. Une application linéaire est une fonction entre deux espaces vectoriels qui préserve les structures vectorielles. Cela signifie que l'application linéaire additionne les vecteurs et multiplie les vecteurs par des scalaires de la même manière que les opérations vectorielles dans les espaces vectoriels eux-mêmes. Un tenseur peut représenter une application linéaire, mais il peut aussi représenter d'autres choses. Par exemple, un tenseur peut représenter une transformation géométrique, une relation bilinéaire entre deux espaces vectoriels ou une distribution de probabilité. Voici quelques exemples de tenseurs qui ne représentent pas des applications linéaires: Le tenseur d'inertie d'un objet représente la résistance de l'objet à la rotation. Il n'est pas linéaire car il dépend de l'orientation de l'objet. Le tenseur de Riemann représente la courbure d'une variété différentielle. Il n'est pas linéaire car il dépend de la deuxième dérivée des coordonnées des points de la variété. Reply ScienceClic Plus · 1 reply @alfredjarry742 2 years ago Sympa la vidéo, je pense qu'elle fera du bien à beaucoup de gens, y compris des profs ce qui est assez triste pour notre pays, mais ta définition n'est pas complète : tu définis ici les tenseurs comme des formes bilinéaires mais c'est beaucoup plus que ça ! UN TENSEUR P-CONTRAVARIANT ET Q-COVARIANT (DONC D'ORDRE N=P+Q) EST UNE FORME MULTILINEAIRE PRENANT EN ENTREE Q VECTEURS D'UN ESPACE VECTORIEL E ET P VECTEURS DE L'ESPACE DUAL E* (DONC P FORMES LINEAIRES DE E) ET Y ASSOCIE UN SCALAIRE. En fait ta défintion affichée en troisième partie se fixe uniquement dans le cas P=0 et Q=2 Source : Mécanique du Continu élement de calcul tensoriel Jean Salençon école polytechnique PAGE 303 https://www.editions.polytechnique.fr/files/pdf/EXT_1245_0_2016.pdf 1 Reply ScienceClic Plus · 1 reply @mrx42 2 years ago Excellent merci ! Reply @arthurbadault6427 6 months ago Merci Reply @quevineuxcrougniard2985 2 years ago Pourquoi parlez-vous de guillemets entre lesquels vous y mettez certaines notions. Quelle est leur signification ? Merci de votre réponse. Reply @futildelalicorne 2 years ago Mais alors, tenseur vs opérateur laplacien, quelle différence ? Reply @jean-baptistelasselle4562 2 years ago (edited) 🙂, et quelle est la définition d'un angle, que vous choisissez, puisque vous prétendez que le produit scalaire de deux vecteurs, ne dépend pas du référentiel choisit? (Puisque vous définissez le produit scalaire à partir de la notion d'angle) Pour le lecteur qui se cassera la tête à essayer de trouver une définition de ce qu'est un angle, voici la réponse : Le concept d'angle est extrêmement intéressant, justement parce que lorsque l'on cherche à la définir, on ressent la profondeur de ce concept... Lorsque nous autres mathématiciens, nous sommes penchés sur le sujet, nous nous sommes mis à réfléchir "naturellement", c'est à dire exactement comme vous, avec notre intuition. Puis nous nous sommes demandés , si l'on oublie notre question, et que l'on se demande "mais finalement, concrètement, lorsque nous raisonnons intuitivement à propos des angles, quelles sont les propriétés de ces choses que nous appelons angles?" "Quelles sont les propriétés minimale qu'il faut connaître à propos des angles, pour être capable de démontrer absolument tout les théorèmes que nous connaissons à propos des angles ?" Je vous le donne en mille, le concept d'angle est entièrement défini dans un espace, pour peu que l'on ait défini un produit scalaire dans cet espace. C'est à dire que le concept d'angle est entièrement défini par une opération purement algébrique . Les tenseurs sont une généralisation du concept de produit scalaire, et on parle d'espace tensoriel. Bien, pour penser réellement, il fait alors terminer un premier tour de cercle, et revenir à la question d'origine : nous sommes partis de notre intuition, en nous disant qu'un angle , ne change pas , suivant le référentiel. Dis plus intuitivement, un angle, entre deux vecteurs, reste exactement le même peu importe "d'où" vous le regardez : que vous soyez au sommet du Puy de Dôme, où à la place de Jaude, l'angle entre deux vecteurs, reste exactement le même. De plus nous savons d'après notre définition que dire qu'un angle entre deux vecteurs, ne varie pas, c'est strictement équivalent à dire que le produit scalaire entre ces deux vecteurs, ne varie pas. Si le produit scalaire entre deux vecteurs, n'a pas changé, alors l'angle n'a pas changé. Si l'angle entre deux vecteurs, n'a pas changé, alors le produit scalaire n'a pas changé. Bien. Autrement dit, lorsque ce monsieur ici présent vous affirme, que l'angle entre deux vecteurs, est invariant, quelque soit le référentiel que vous choisissez, ce monsieur en réalité vous enferme dans une affirmation qui reste à prouver : celle que l'espace dans lequel nous vivons est un espace euclidien, c'est à dire un espace vectoriel, munit d'une opération, appelée produit scalaire, qui en plus des propriétés algébriques qui le définissent, a la propriété d'être invariant par changement de référentiel. Il manque donc à ce monsieur, pour être rigoureux, le fait de définir ce qu'est un référentiel, dans un espace euclidien : Ce monsieur a en quelque sorte raison, parce qu'il s'appuie sur le fait que votre perception usuelle d'humain "ressent", le monde comme étant un espace vectoriel euclidien, mais qui nous dit que notre intuition ne nous trompe pas ? Que ce que nous ressentons n'est pas une illusion ? Pour s'en assurer, il faut raisonner, s'apercevoir que finalement, tout ce que dit ce monsieur repose sur la supposition, que notre Monde a la géométrie d'un espace vectoriel euclidien. Et se dire que rien ne dit que cette supposition n'est pas fausse. Pour le vérifier, que notre Monde a une géométrie qui est celle un espace vectoriel euclidien, il faut faire des expériences, dont les résultats doivent au moins ne pas contredire cette supposition. Allons, la question est vaste alors pour faire de petites avancées en la matière, ce que nous allons faire, c'est d'essayer de trouver une expérience qui arrive à contredire cette supposition, que notre Monde a une géométrie d'espace vectoriel euclidien. Et pour essayer de trouver une telle contradiction, nous pouvons faire par exemple, ceci : Essayer d'imaginer un espace géométrique qui n'est PAS, euclidien. Par exemple, un espace dans lequel ... Dans lequel la somme des angles d'un triangle n'est pas égale à 180degres . Sans en donner les détails, on peut en effet imaginer des espaces géométriques dans lesquels la somme des angles d'un triangle n'est "presque jamais, égale à 180degre (pi). Un exemple de telle géométrie est la géométrie riemannienne. Une autre possibilité, serait d'essayer de définir un espace géométrique, dans lequel , au contraire de ce que dit monsieur, l'angle entre deux vecteurs, varie, en fonction du référentiel choisit. Autrement dit un espace dans lequel le produit scalaire de deux vecteur varie, en fonction du référentiel choisit. Cela est-il concevable ? Je pense que oui, et alors la nouvelle opération algébrique définissant ce qu'est un angle, ne serait plus un produit scalaire, ou un produit vectoriel, mais autre chose. Voyons essayons de trouver, un tel "autre chose". Ok, pour définir un angle, on défini une opération entre deux vecteurs, qui donne un résultat. Le résultat de l'opération, s'il ne varie pas en fonction du référentiel, rendra le concept d'angle absolument invariant par changement de référentiel, peu importe quelle est cette opération. Ok, donc on cherche une opération, entre deux vecteurs, dont le résultat varierai en fonction du référentiel choisit. C'est là qu'on a besoin de définir précisément la notion de référentiel . Soyons bien clair nous choisissons deux vecteurs bien précis, et on cherche une opération que l'on peut faire avec ces deux vecteurs, dont le résultat variera en fonction du référentiel choisit. Autrement dit, le résultat de l'opération ne doit plus être une simple "valeur fixe", mais une fonction du référentiel : Au lieu d'une opération de type : V.W = k, où k est un nombre réel (ou complexe?) On veut un opération de la forme suivante : V.W = f(R) , où f est une fonction, de l'ensemble de tous les référentiels, dans l'ensemble des nombres réels (ou complexes?) De plus, on veut que f ne soit pas une fonction constante. Alors nous y voilà, il va bien nous falloir définir précisément, ce que l'on entend par referentiel, pour pouvoir trouverun exemple de telle fonction f(R).... J'insiste sur le fait que je ne suppose rien d'autre sur f(R), que le fait qu'elle ne soit pas constante, en particulier pour les initiés à la mathématique, je ne suppose en rien qu'elle soit continue, pqd même un homomorphisme d'une quelconque structure. Bien bien bien. Alors, peut on trouver comme cela, dans la nature, une fonction non constante, qui associe à deux référentiels différents, deux nombres réels (complexes?) différents ? Hm ..... Allez, cherchez, qu'est ce que l'on a imaginé depuis longtemps, qui soit un nombre réel, et qui varie en fonction du référentiel de l'observateur (en particulier de l'accélération du référentiel) ? . Bien, je vous laisse chercher une telle fonction f(R), Et mon point est donc de dire, que ce que ce monsieur affirme, que l'angle entre deux vecteurs est invariant par changement de référentiel, reste à prouver, et qu'aucune démonstration de ce fait n'est donnée dans la présente vidéo, intéressante, puisqu'elle me permet d'écrire ce que je viens d'écrire. Prenez simplement conscience que ce que ce monsieur affirme, revient à supposer que notre Monde a bien la géométrie d'un espace vectoriel euclidien, ce qui est fort réducteur, face à l'imagination que vous pouvez réellement avoir, et qui reste à prouver, quand bien même cela serait une approximation tout à fait raisonnablement utilisables dans bien des domaines d'ingénierie, mais pas tous, comme la cartographie et la technologie GPS Merci à l'auteur de cette vidéo, très sincère, et ouvrant une discussion/réflexion fort intéressante ! Pour la note d'humour, j'ai utilisé cette discussion pour comprendre ce que ces satanés ingénieurs travaillant dans l'intelligence artificielle font, et qui se cache derrière eux, car eux, ne comprennent absolument rien à la mathématique, malgré tout ce qu'ils peuvent affirmer, comme une écrasante majorité de scientifiques d'autres domaines que la mathématique. (Mais pourquoi est-ce qu'il appelle t ce truc "TensorFlow", ces abrutis...???) 1 Reply 1 reply @pierremihalic9178 2 years ago Bonjour, dans presentation d un tenseur comment vous montrez qu un vecteur est un tenseur? Dommage que vous ne terminez pas la vidéo par le lien avec la relation de changement de repère... 3 Reply 1 reply @antoinet1304 2 years ago En fait quand j'étais en prépa (96-99) j'ai rien compris aux tenseurs. y'a pas une image (aka explication imagée) de "tendre" un truc ? là, à mon âge (44) je vois des "tordeurs" facilement, et en plus j'étais doué en algèbre. bref peut être que je m'explique comme un noob ^^ Reply @miloudeboukra3994 2 years ago Miloud Reply @noe851 2 years ago Bonjour, y'a t'il une différence entre un tenseur d'ordre n et une application n-linéaire ? Merci pour la vidéo 👍 3 Reply 1 reply @bouhschnou 2 years ago T est-il le "tenseur du produit scalaire"? Reply @samdob9832 2 months ago alors c est quoi un anneau tenseur Reply @pierremihalic9178 2 years ago Bonjour, merci pour votre vidéo. Je vous ai envoyé un commentaire pour savoir comment vous feriez à partir de ce point de vue sur les tenseur pour montrer qu un vecteur est un tenseur. Je serai content d avoir une réponse... Dans l attente merci 2 Reply ScienceClic Plus · 2 replies @skaffen 6 months ago Non, contrairement à ce que tu dis, la définition du début est valable (et c'est même la définition wikipédia) parce qu'il n'existe pas de matrice qui n'ait pas une interprétation géométrique. Tout ensemble de points a un équivalent géométrique, d'ailleurs la géométrie arrive très loin dans la hiérarchie des fondements mathématiques (théorie des ensembles). C'est absurde, un vecteur n'est pas autre chose qu'une liste de nombres, c'est l'utilisateur qui interprète ou non cette liste, en fonction de l'utilisation. C'est comme si je disais que le nombre 23 n'est pas une vitesse, ou n'est pas une température. Question de point de vue. Tu n'as pas l'air de réaliser que les objets mathématiques peuvent être représentés de nombreuses façons différentes. Quand tu dis qu'un vecteur est une flèche, tu fais un choix arbitraire de notation, qui ne regarde que toi, mais le vecteur c'est un concept, pas une notation. D'ailleurs tu le dis toi-même, un couple de deux nombres peut décrire n'importe quoi...donc notamment un vecteur ! Tu as bien fait de mettre des guillemets dans la description sur ta "vraie" définition du concept. Reply @77kiki77 2 years ago (edited) Pourrait-on dire que le déterminant de 2 vecteurs est un tenseur (det |u ; v|) ? 3 Reply 1 reply @ryzenrog1139 2 years ago (edited) Superbe vidéo ! Cependant, je ne suis pas d'accord avec la définition que tu donnes d'un vecteur. Un vecteur, c'est un élément d'un espace vectoriel, rien de plus, rien de moins. C'est simplement l'élément d'un espace vectoriel, et systematiquement lui associer une signification géometrique (ce que tu sembles supposer au début de la vidéo), ou à l'assimiler à ses coordonnées sous forme de matrices colonne (ce que tu critiques), c'est un poil relâché. Seule la définition compte, et en ce sens, il n'est pas nécessaire de donner une représentation géométrique d'un vecteur. Je comprendrais néanmoins que tu aies fait le choix d'assimiler les vecteurs à des flèches et leurs propriétés géométriques par souci de pédagogie. 1 Reply ScienceClic Plus · 1 reply @pierremihalic9178 2 years ago Bonjour, merci de cette vidéo. Dans cette présentation des tenseur comme vous montrez qu un vecteur est un tenseur.? 1 Reply 1 reply @arthurdurand4098 2 years ago Bonjour comment on fait le lien entre la définition du tenseur métrique comme etant le produit scalaire et l’approche selon laquelle la métrique donne la distance entre 2 points avec une sorte de « théorème de pythagore généralisé » ? (Comme on peut le voir ds ta série de vidéo sur la RG, l’épisode 4) 2 Reply ScienceClic Plus · 2 replies @dobotube 2 years ago Super video comme d'hab ! Petite correction: c'est pas vraiment juste de dire que le produit scalaire ne dépend pas du tout du repère (14:36). Il est insensible aux rotations de repère mais les étirements du repère l'affecte. 1 Reply ScienceClic Plus · 5 replies @lexgrd 2 years ago Hey super video je voulais savoir ce que vous faite comme étude ou métier 1 Reply ScienceClic Plus · 1 reply @brahimsorroche4075 2 years ago (edited) T = nuage / '' '' '' \ pluie = Temps T sa chance Reply @EW-mb1ih 2 years ago Tout à la fin de la vidéo (24:50), qu'est ce que tu entends par le "tenseur en tant qu'objet géométrique n'a pas changé"? 1 Reply ScienceClic Plus · 1 reply @eltongravilra1762 2 years ago Je suis bac+2 prépa et je trouve la vidéo plutôt accessible. 5 Reply 1 reply @mok6034 2 years ago Le déterminant est donc un tenseur 2 Reply ScienceClic Plus · 1 reply @l_urent 1 month ago Ok compris. Une question : les normes impliquées lors du calcul d'un produit scalaire dépendent de la graduation choisie, non ? On a là un élément (constitutif d'un repère) qui est abitrairement choisi et qui, pourtant, préside au calcul du tenseur. N'est ce pas contradictoire avec la définition enseignée dans cette vidéo ? 1 Reply ScienceClic Plus · 1 reply @jean-baptistelasselle4562 2 years ago Non pas linéarité, mais bi-linearite Reply @oganseprodjephte4609 2 years ago Pourquoi il n'y a plus de vidéo sur chaîne science clic 1 Reply ScienceClic Plus · 1 reply @vinceguemat3751 2 years ago géniale, je veux une suite ! Pourquoi le produit scalaire correspond a la matrice unité ? Que représente les différentes opération matricielles en tant que tenseur ? comment a partir de la matrice on fait des "calculs matricielles" qui aboutissent a l'application du tenseur a 2 vecteurs ? Reply 3 replies @jamelbenahmed4788 2 years ago Donc un tenseur est simplement une forme multilinéaire sur un espace vectoriel, si j’ai bien suivi 1 Reply ScienceClic Plus · 1 reply @sidiabdelhaksbai6422 2 years ago Un tenseur est annulé si la terre est élastique Reply @mehdimabed4125 2 years ago (edited) Très bonne vidéo merci ! Par contre je ne suis pas sûr d'avoir saisi une ou deux subtilité : 1) La définition d'un tenseur me semble être strictement identique à la définition d'une application linéaire... Il n'y a donc aucune différence entre ces deux concepts ?! 2) Dans le cas du produit scalaire, sa valeur est indépendante du repère, très bien, mais les valeurs qui le constituent (norme des vecteur et angle entre les vecteur) me semblent être relatives au repère choisi, donc est-ce que cela signifie qu'il y a un lien fondamental (géométrique) entre angle et norme ? L'angle entre deux vecteur serait donc toujours égal (quelque soit le repère) au rapport du produit scalaire (qui est un invariant) avec le produit des normes,et qu'il y aurait donc un lien direct entre angle et longueur ? Je dis sûrement des bêtises alors n'hésitez pas à me corriger ^^ 2 Reply 4 replies @ThomasLomba 1 year ago ta définition est incomplète: tu as seulement définit un tenseur d'espèce (0 2) sur R, càd une forme bilinéaire. Mais en général un tenseur d'espèce (p q) c'est une une application p+q-linéaire qui est défini sur le produits V1* x ... x Vp* x W1 x ... x Wq --> K où V1, ..., Vp, W1, ..., Wq sont des espaces vectoriels sur K. Reply @elight1141 2 years ago Merci ! Je me demande pourquoi il y a pas mal de physiciens qui sont allergiques à la rigueur mathématique... 4 Reply 2 replies @Fine_MoucheTache 2 years ago 15:00 j'ai l'impression que la norme diffère d'un référentiel / de coordonnées à un / d' autre(s) : (5,3) (référentiel/coordonnées rouge(s)) et (1,2) (référentiel/coordonnées bleu(s) ) ne donnent pas la même longueur d'hypoténuses . :/ 1 Reply ScienceClic Plus · 2 replies @Fine_MoucheTache 2 years ago Que penses-tu de cette vidéo qui explique les tenseurs, tombe-t-il dans l'un des 2 pièges que tu énonces au début ? https://www.youtube.com/watch?v=f5liqUk0ZTw (name: What's a Tensor / yt channel : Dan Fleisch ) 1 Reply ScienceClic Plus · 1 reply @doekia 2 years ago J'en arrive à la conclusion que le tenseur (les termes (Txx Txy Tyx Tyy)) est finalement une représentation du repère de coordonnées. Ai-je juste ou c'est encore plus subtil ? 1 Reply ScienceClic Plus · 1 reply @nicolasmenotti 2 years ago Il y a quand même un isomorphisme entre les vecteurs plan et R^2. 1 Reply ScienceClic Plus · 2 replies @arthurdurand4098 2 years ago Bonjour merci pour la vidéo ! J’ai une question: vous dites qu’un tenseur ne dépend pas des coordonnées qu’on choisi. Hors j’ai cru comprendre que le tenseur métrique donnait la distance entre deux points en fonction de leur écart de coordonnées et parfois en fonction de leur coordonnées. Donc le tenseur métrique dépend des coordonnées puisqu’il s’exprime en fonction de ces dernières non ? 2 Reply ScienceClic Plus · 4 replies @Cax36940 2 years ago Il y a une différence entre les tenseurs et les formes linéaire/multilinéaire ? 1 Reply ScienceClic Plus · 2 replies @micper5507 2 years ago à 11:43 il faut remplacer T(w,v) par T(w,0). Reply ScienceClic Plus · 1 reply @fawzibriedj4441 2 years ago Le couple (3;5) est bien un vecteur (et non juste une représentation d'un vecteur) car il appartient à l'espace vectoriel des couples de réels, qui satisfait tous les axiomes d'un espace vectoriel. Pareil pour la définition qu'on voit au lycée du produit scalaire comme étant = ux.vx + uy.vy Elle satisfait tous les axiomes du produit scalaire, axiomes qui n'imposent pas une indépendance aux coordonnées. La vidéo donne une autre manière de se représenter un tenseur, ce qui est toujours positif car ça nourrit l'imagination. Mais ça ne veut pas dire que des définitions qui se basent sur des coordonnées sont fausses ! 1 Reply ScienceClic Plus · 5 replies @brahimsorroche4075 2 years ago (edited) Travail ( +,-- ) = la vie ? Sa vie... Reply @emiliengarcia4816 2 years ago Bonjour, À 16:28 vous dites que le tenseur est un opérateur qui ne dépend pas du repère et donc du système de coordonnées choisi. Seulement dans l'exemple du produit scalaire, celui-ci fait intervenir la norme qui dépend du repère. Reply 1 reply @rubengirona1898 2 years ago Ducoup toute les applications linéaires qu'on voit sur les espaces vectoriels (les morphisme, endomorphisme, automorphisme) sont des tenseurs ? Reply ScienceClic Plus · 1 reply @danielplatteau5137 2 years ago ceci est ( interruption publicitaire ) intéressant mais ( interruption publicitaire ) nécessite un peu ( interruption publicitaire ) de concentration, si vous ( interruption publicitaire ) voyez ce que je veux dire ... Reply @bozo1354 2 years ago (edited) Petite question. Quand il est écrit T(u,v) appartient à R, est-il juste de l'ecrire aussi de cette manière : T(u,v) appartient à R², considérant alors que u et v sont réel ? 1 Reply 3 replies @benj6964 2 years ago Y a-t-il une différence entre un tenseur et une forme n-linéaire ? 1 Reply ScienceClic Plus · 4 replies @eliasp.2759 1 year ago 12:10 Ne s’agit-il pas de la définition d’une forme multilinéaire plutôt ? Reply ScienceClic Plus · 1 reply @noeldeuxmillevingt4798 1 year ago Le produit scalaire est un tenseur d’ordre deux, ok. Mais est ce que c’est le seul tenseur d’ordre deux ou juste un parmi d’autres...? Merci pour l’eventuelle reponse Reply 1 reply @abinadvd 2 years ago Pas radin en pub. Reply @mathoph26 2 years ago Donc en gros un tenseur c'est juste un produit scalaire non symétrique, non positif-défini ? 1 Reply 5 replies @yapadek3098 9 months ago Super ! Mais quelle utilité ont ces tenseurs ? Reply 2 replies @antoine2571 3 months ago Je suis un pru déçu honnêtement je m'attendais à ce que ca aille (BEAUCOUP) plus loin Pour ceux qui ont déjà fait des maths, je vais vous faire gagner du temps Un tenseur d'ordre n c'est une application n-lineaire et elle est donc entièrement déterminée par son action sur les vecteurs de base de l'espace vectoriel. On représente ces valeurs dans une matrice (un peu comme la matrice d'un produit scalaire donne les produits scalaires des vecteurs de la base, d'ailleurs un produit scalaire est un tenseur d'ordre 2) (C'est pas dit dans la vidéo mais les produit scalaires sont exactement les formes bilinéaires symétriques. C'est à dire quun tenseur d'ordre 2 symétrique c'est un produit scalaire (la réciproque est triviale)) Reply @jcpascal6548 2 years ago Un tenceur , c'est un Penseur avec 2 faute orthographe 😂🤣 Reply @lecodeurfute4287 3 months ago Bref c'est juste une forme multilénaire mais remasterisée à la sauce "physicienne". 😂 Reply ScienceClic Plus · 1 reply @hassantahri973 1 year ago Vous parlez pendant tout ce temps et vous êtes incapable de posez une définition correcte. Je suis désolé. Il fallait dire .T est un danseur est la donnée de ....etc.. Reply @diezelle57 3 months ago Si la notion de tenseur est éclaircie, rien n'est dit sur son utilité ou sa nécessité en physique relativiste. ScienceClic Moins ? Reply ScienceClic Plus · 1 reply @Annabelledelrio 2 years ago Poussif Reply @kantanlabs3859 2 years ago C'est beaucoup plus sobre que par le passé. C'est aussi nettement plus rigoureux. Ça reste une approche essentiellement mathématique (formes multilinéaires et algèbres associées), dont vous ne précisez pas le domaine d'application dans le cadre des sciences en général, ce qui laisse la porte ouverte à de nombreuses dérives d'interprétation. Pour le scientifique, ce domaine, aussi séduisant soit-il pour le mathématicien, se limite aux cas rarissimes où des lois au caractère fondamentalement empirique (résultant de l'expérience et de l'observation) peuvent être approchées par des formes linéarisés. L'étude générale du simple pendule pesant ne peut se faire dans un tel cadre. De mème en mécanique des milieux élastiques, l'approche tensorielle se limite aux très petites élongations (étude des ondes de petites amplitudes). Reply @geraldinejasnin7378 2 years ago ou la la !! youtube nest pas fait pour faire des cours bac +5!!! regardez les videos de DAVIS louapre ou Etienne KLEIN !! prenez des cours de vulgarisations !! imbuvable Reply ScienceClic Plus · 3 replies @brahimmustapha4601 2 years ago Nul comme explication Reply Top is selected, so you'll see featured comments

Tensors Explained Intuitively: Covariant, Contravariant, Rank

Tensors Explained Intuitively: Covariant, Contravariant, Rank Physics Videos by Eugene Khutoryansky 1.04M subscribers Subscribe 26K Share Ask Save 1.3M views 8 years ago Tensors of rank 1, 2, and 3 visualized with covariant and contravariant components. My Patreon page is at / eugenek 1,294 Comments rongmaw lin Add a comment... Pinned by @EugeneKhutoryansky @EugeneKhutoryansky 6 years ago To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email. 110 Reply Physics Videos by Eugene Khutoryansky · 8 replies @FredyeahEternal 8 years ago As a hobbyist mathematician you have no idea how valuable these videos are, please dont stop making them, you're helping people be smarter 1.1K Reply Physics Videos by Eugene Khutoryansky · 13 replies @ianpool4330 8 years ago I've spent so much time trying to find a simple explanation of covariant and contravariant vectors online, and in the first 3.5 minutes you've managed to out perform anything I've come across. A well deserved round of applause to you, Eugene! Keep up the great vids! 637 Reply Physics Videos by Eugene Khutoryansky · 9 replies @amoghskulkarni 6 years ago Chronicles of tensors: the musical 266 Reply 1 reply @matt1285 7 years ago The music when you got to rank 3 made me laugh 23 Reply @MrTiti 8 years ago our great classical music adds so much drama to on otherwise sober topic 117 Reply @josh3658edwards 8 years ago (edited) This channel is honestly top notch. Most resources are either too simplified to the point where they are not useful to someone who actually needs to learn this material, or they are so dense that a new learner gets lost in the details and misses the big picture. You do a great job at making the point clear (with the aid of amazing visuals) while also keeping everything accurate. Seriously, this is world class educational material. Get more famous! 80 Reply Physics Videos by Eugene Khutoryansky · 2 replies @black_wolf365 6 years ago (edited) The professors I had in the university while doing my Bachelors all failed to explain the concepts of covariant contravariant in an understandable manner. You have done what they have failed to do in less than 12 minutes! :D #RESPECT 103 Reply @kimweonill 2 years ago Your combination of graphics, content and music is otherworldly 😊 7 Reply Physics Videos by Eugene Khutoryansky · 1 reply @AndrewBrownK 7 years ago FINALLY A HELPFUL VISUAL REPRESENTATION!! I’ve been stuck on intuiting covariant vectors for YEARS! I think I get it now, it’s the components of the vector that are really covariant or contravariant, not the invariant/intrinsic vector itself 16 Reply @umeng2002 7 years ago Having a good instructor makes a night and day difference when learning more advanced subjects. Great video. Making the jump from just dealing with vectors to tensors trips up a good number of people. 9 Reply @EugeneKhutoryansky 8 years ago If you like this video, you can help more people find it in their YouTube search engine by clicking the like button, and writing a comment. Thanks. 201 Reply 9 replies @tiuk23 8 years ago Your channel should be promoted by some other famous channels, like Vsauce. Your videos are just too good. 3Blue1Brown got promoted this way. Maybe one day, this channel will as well. 328 Reply Physics Videos by Eugene Khutoryansky · 10 replies @grittychops6755 4 years ago The music is freaking me…… 5 Reply @alexanderthegr888 5 years ago The music makes this the most stress intense tensor video anime show I have ever seen in my life. 7 Reply @kbwsoikat 3 years ago You tube amazing because of the people like you who believe that knowledge should be free. 4 Reply Physics Videos by Eugene Khutoryansky · 1 reply @JayLikesLasers 8 years ago Excellent introduction to tensors. It's funny how you could complete a whole masters or PhD and never see these any more than a 2d drawing of these mathematical objects, but then a video comes along and in under 12 minutes shows you what it took so long to wrap your head around to imagine. 110 Reply Physics Videos by Eugene Khutoryansky · 2 replies @DarkFunk1337 8 years ago I wish you had uploaded this when I was taking Continuum Mechanics! 6 Reply @MrRobertT03 8 years ago Eugene, your videos are absolutely incredible. Thank you for doing such a great job making things so well-explained and intuitive! 15 Reply Physics Videos by Eugene Khutoryansky · 1 reply @therealDannyVasquez 8 years ago I didn't even know this was a thing! Amazing 😀 13 Reply @descheleschilder401 7 years ago Despite this being a great animation (like the one about Fourier transforms, which is even much better) this video I feel an inconsistency lurking with regard to the statement that the dot product decomposition is covariant. Let's take the most simple example of three orthogonal basis vectors and an arbitrary vector (like the situation around 20 seconds in this video). Now all the components of this vector are the dot product (orthogonal projections) with (on) the basis vectors. So if you make the basis vectors x times longer (or shorter) and giving this new basis vector the value 1 the components of the vector become x times as short (or long). But because the components are the dot product with the basis vectors, also the dot product decomposition becomes x-times as short, and this result is passed on to the case where the basis vectors are not orthogonal. Look for example at the video at around 2:58, where it is said that if you make the basis vector twice as large the dot product becomes twice as large too, but the basis vector you make twice as large gets again the value 1 and the corresponding vector component becomes twice as small (like is explained earlier: if you make the base vectors twice as large, the vector's components get twice as small), so each of dot product of the vector components with the basis vectors becomes x times smaller (larger) if you make the basis vectors x times larger (smaller), hence contravariance. A good example of a covariant vector follows from the (x,y,z) vector. This is a contravariant vector, but the (1/x,1/y,1/z) vector is a covariant one. More concrete, the wavelength vector [which corresponds to (x,y,z)] is a contravariant vector while the wavenumber vector, the number of waves per unit length, is a covariant vector [which corresponds to (1/x,1/y,1/z)]. See Wikipedia's "Contravariant and covariant" article. 10 Reply @SuperTubbyTube 3 years ago The music selection at 8:24 for the rank 3 tensor is HILARIOUS!! 😂 Start at 8:14 and wait for it! 2 Reply @p72arroj 6 years ago Really good video, you've done that people can visualize something which many professors didn't get in many years with their students and tried to explain as a teachers a visual concept with lots of usefuless words and few quality visualizations. Thanks 6 Reply @tariq3erwa 4 years ago Wow, the only video about tensors where I actually understand everything 1 Reply @malm7arb 8 years ago I have never clicked on a notification this fast before..... 133 Reply 3 replies @owenloh9300 8 years ago Wtf i was trying to find the answer for this on the net and this just popped out in my notifications -crazy 49 Reply Physics Videos by Eugene Khutoryansky · 4 replies @BarriosGroupie 5 years ago Great video. I prefer defining a covariant vector via its dot product with the corresponding contravariant vector being an invariant. This is how Tullio Levi-Civita defined it in his famous book, used by Einstein in his 1917 GR paper. 5 Reply @dzanc 7 years ago (edited) Explenation of rank 3 tensor William Tell overture ensues ayy lmao 4 Reply @PM-et6wz 8 years ago You need to get your name out there. You should talk to other popular youtubers for support. Your videos are incredibly unique and informative, more people need to watch them. Professors should also be using your videos as to tool to teach students. 6 Reply @gruminatorII 7 years ago Absolutely phenomenal video, i really wish we had these to study 8 years ago. I finally understood the difference between co and contravariant .... before i just knew the definition 3 Reply @Born2Lose_LiveToWin 3 years ago Omg, this channel is a Gold mine for upper division classes. Again thank you so much. You’re helping me with Quantum mechanics and Electrodynamics! Specially as a nonverbal visual learner this really helps! 3 Reply Physics Videos by Eugene Khutoryansky · 1 reply @mh-no5it 8 years ago Any day is a good day when one of these videos get published. Reply @probiner 8 years ago I was looking into tensors 3 days ago and couldn't wrap my head around them and your video nailed it for me! Thanks a lot! Let me see if you have one on Quaternions, your skills might just finally break the wall for me to grasp how they are beyond Axis/Angle rotation and why if the axis is not normalized with a quaternion I get a skewed transform! Keep up! 4 Reply @qazmlp-jz3gt 2 years ago Holly shit I understand it !!!! Thanks!! 2 Reply Physics Videos by Eugene Khutoryansky · 1 reply @ivanbykov7649 8 years ago the music is epic 34 Reply 2 replies @Insertnamesz 8 years ago These videos are consistently enlightening. They should be part of curriculum. Well done! 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @delawarepilot 8 years ago Great videos. I can't wait to see the one on Einstein's field equation 19 Reply @manodura8132 3 years ago Many thanks for this wonderful video/explanation 🙏 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @jameshuang9568 6 years ago Thanks you for the exlanation. It helps me clear tons of mistaries! However, I am still a bit confused about the covariant component at 2:58. If the resultant vector remains constant and the base vectors are doubled in length, shouldn't the value of the components be decreased in order the result in the same vector? Please correct me if there's any misunderstanding. 14 Reply 2 replies @samaraliwarsi 8 years ago I'm gonna wait for the next episode like I wait for the next episode of my favorite series. Great Job!!! Thank you so much for this :) 2 Reply @zarchy55 8 years ago As always, the most excellent video! 11 Reply Physics Videos by Eugene Khutoryansky · 1 reply @sdsa007 6 months ago wonderful stuff! I had learned what a covector/one-form/differential/covariant vector is and i had to watch this again to understand and visualize the dot-product basis vectors Reply @SliversRebuilt 8 years ago THANK YOU SO MUCH, YOU ABSOLUTE SAGE AMONG MEN 15 Reply Physics Videos by Eugene Khutoryansky · 2 replies @b4lrogd 1 year ago The music hits hard 1 Reply 1 reply @EugeneKhutoryansky 7 years ago You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: http://www.youtube.com/timedtext_video?v=CliW7kSxxWU&ref=share You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at https://support.google.com/youtube/answer/6054623?hl=en Thanks. 41 Reply 5 replies @quantumworld9434 4 years ago Great video. Now I got a clear concept about tensor. This is the best video in YouTube to get a visualization of tensor physically. 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @Steven22453 6 years ago I've literally spent several years trying to understand tensors through self-studying to no avail. Your videos are the most intuitive and easy-to-understand way I've found and for the first time, I actually feel like I have a good understanding of tensors. 2 Reply Physics Videos by Eugene Khutoryansky · 1 reply @pedromenezesribeiro7 8 years ago Finally someone could explain in a concise and clear manner what covariant and contravariant components are! Thanks a million! Reply @MrJesuswebes 8 years ago (edited) Just a humble piece of advice: I think music should be more "subtle". Orchestral music is beautiful but I think it can "bother" a little when you try to concentrate on explanations. Of course: this is my point of view, of course. 335 Reply 21 replies @ericgarcia9769 2 years ago This is by far the best explanation about tensors that I could find. This has helped me tremendously for my general relativity class. Thank you so much!!! 2 Reply Physics Videos by Eugene Khutoryansky · 1 reply @francissanguyo2813 8 years ago Hmm... I would like to see a video regarding the Navier-Stokes Equations... somewhere in the future. 17 Reply Physics Videos by Eugene Khutoryansky · 3 replies @Carleytanner653 7 years ago Also, I liked the music :) It matched the excitement I felt at finally understanding this! 2 Reply @blackriver2531 8 years ago 51 people accidentally clicked dislike. 8 Reply 2 replies @prenomnom5057 7 years ago Simply EXCELLENT. I never post comments on YouTube but this deserves to be the TOP video in any search on the topic. 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @Jabber_Wock 8 years ago (edited) This is a great video, thanks Eugene and Kira! I understand your description of contravariant vectors, and how a vector can be represented by a contravariant combination of basis vectors. It would be great if you could elaborate on how a vector can be represented by a combination of dot products of arbitrary basis vectors. Perhaps "dot product" needs to be defined first (and "angle")? 3 Reply 1 reply @kevinbyrne4538 7 years ago For DECADES I've searched for an explanation of tensors that's as simple as the one that you've presented here in less than 12 minutes. Thank you, thank you, thank you ! I am in your debt. 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @banshee511 8 years ago I love the video! However, the music is too good. It is really distracting. 9 Reply @maurocruz1824 7 years ago I simply can't understand why this topic in the books is so entangled and you just made up so easy! Reply @qbslug 8 years ago so what is the difference between the 2nd rank tensors produced with covariant, contravarient and combination vectors?!? 7 Reply 2 replies @taitywaity1836 8 years ago It's sad the amount of people who saw one of your videos and subscribed, but didn't continue to watch your new videos. You deserve way more views per video than you are getting on average, especially considering how many people thought you were worth a sub. 2 Reply @xgozulx 8 years ago Your videos are so awesome. Note. I've never used super index values as you showed, I alwais use sub indexes 3 Reply 1 year ago So good. But it would be even better without that music that avoid concentration on the topic. 1 Reply @fawbri2654 7 years ago Hi,Thanks for the video and the explanations.In the beginning of the video you say "if we double the length of the basis vectors, the dot product doubles" if V = (2, 0) in the basis e1 = (1, 0), e2 = (0, 1), V.e1 = 2 But if e1' = (2, 0), V in the new basis would be V = (1, 0), and V.e1' = 2 So why didn't you express V in the new basis for the dot product but you did it for the normal components of V ? 5 Reply 1 reply @Carleytanner653 7 years ago Thank you so much. I've been trying to get some sort of intuition for what a tensor is, and this is definitely the best video I've found to help me with that. 2 Reply @MrPetoria33 8 years ago I highly recommend the videos by Prof. Pavel Grinfeld (MathTheBeautiful) for more on this subject, as well as his textbook, which focuses on geometrically intuitive approaches to this subject. Prof. Bernard Schutz's books are also excellent, though they require more mathematical maturity on the part of the reader. 3 Reply 1 reply @pendalink 8 years ago Naturally, just as I start to learn about tensors, you release this. Thank youuuuuuu 2 Reply @muzammalsafdar1 8 years ago best explained 2 Reply Physics Videos by Eugene Khutoryansky · 1 reply @naba5850 8 years ago Perhaps you have no idea how valuable your videos are to us Reply @Ricky-zc8qm 7 years ago V and P for the Tensors, Yes yes, I can sense their relationship, subliminally they will become one. 3 Reply @jcave8580 5 years ago I am learning tensors by myself and this has been the most incredible explanation of covariant and contravariant components. Thanks for this work. It´s great! 2 Reply Physics Videos by Eugene Khutoryansky · 1 reply @nogmeerjan 8 years ago I seem to miss the dot product knowledge to understand the story :-( Maybe a good idea for a future video? 14 Reply Physics Videos by Eugene Khutoryansky · 3 replies @inotmark 4 years ago Rossini was so interesting i found it difficult to concentrate, but it was an extremely humorous moment when the third rank was added to the tensors as the cavalry came charging over the hills.... 1 Reply @MuggsMcGinnis 8 years ago (edited) The contra-variant components are shown graphically to be related to the vector's length but the co-variant components are not. It doesn't show how one could derive the vector from the co-variant basis vectors which can apparently be multiplied to any size without changing the vector they define. When the covariant components were increased or decreased, the vector was unchanged. 6 Reply 1 reply @pronounjow 8 years ago (edited) This video should be on YouTube's trending page. Reply @asterisqueetperil2149 8 years ago I am a bit confused by your statement about the covariant components. If you double the length of your basis vector, the scalar product with the basis vector (so your covariant components) will be divided by 2 and not multiplied ? Or if you don't set the new length as the new unit but just multiply by 2, then the scalar product remain the same ? In my understanding of tensors, the contravariant basis (ie the covariant components) was defined by the invariance of the covariant-contravariant product, that is by the metric tensor. May you clarify this point for me please ? And keep up the good work ! 12 Reply 2 replies @vector8310 8 years ago Astonishing clarity on a congenitally obscure topic Reply Physics Videos by Eugene Khutoryansky · 1 reply @Intrebute 8 years ago In the video you mention that the same rank 2 tensor composed of two vectors can be described as various combinations of covariant and contravariant components of those two vectors. My question is, are these different representations completely determined by each other? For example, if you have a rank 2 tensor T, which you know was composed by the covariant components of a vector P and the contravariant components of a vector V, can you tell what the representation would be if you wanted it to be composed of the contravariant components of P and the covariant components of V, instead? Even if you don't know the actual vectors P and V but only the tensor T? Another question is, all these representations composed from different combinations of "variances" of some component vectors P and V feel like they would all be 'nicely' related to each other. Kind of how different basis vectors give different different representations of the same vector. Do all these combinations form a nice structure, similar to how vectors are still vectors despite the choice of basis used to represent them, if any? 3 Reply Physics Videos by Eugene Khutoryansky · 1 reply @AntaresXAndromeda 8 years ago We're lucky to have you on YouTube. Reply Physics Videos by Eugene Khutoryansky · 1 reply @palpytine 7 years ago Suppose we just shove some numbers together in some particular order. Not going to say *why*, but hey... at least they're swaying constantly. Suppose we then claim this to be intuitive. 8 Reply 1 reply @kevinliou1 6 years ago (edited) I saw the taiwaness sub and it's very good for those who are Chinese to see the excellent video. Thank you, Vera Wu. 2 Reply @cliffpetersen6881 5 years ago (edited) Thank you for the clarity - the music does get in the way however, would you consider making it much softer or not having it at all? 9 Reply @AlaminArebo 8 months ago good but the sound was disturbing 1 Reply @SupremeCommander0 8 years ago what is geometrically a dot product of two vectors ab? aside of the area |a|cosf x |b|cosf, what does it mean? 4 Reply Physics Videos by Eugene Khutoryansky · 4 replies @mathsbyazharsir3415 1 year ago Pls don't stop making video it's really helpful Reply Physics Videos by Eugene Khutoryansky · 1 reply @ΖήνωνΕλεάτης-δ7κ 8 years ago The bleeding obvious, repeated over and over, under nut-cracking classical miuzak! 7 Reply @lancelovecraft5913 8 years ago I have been waiting for this video since I first learned of tensors 2 years ago. Thank you 1 Reply @tempestaspraefert 7 years ago Information density is a bit low, even when on 2x speed. The constant movement of the "3d objects" is a bit unnecessary. I still hit that like button, because the matter discussed is quite abstract and the explanation splendid! Well done ;-) 16 Reply 1 reply @eqsventurebuilder2409 2 months ago Sin dudas esta es una de muy pocas explicación de #Tensors {#escalares, #vectores, #matrices} más didácticas que jamás haya visto y que no pierda consistencia teórica y satisface por igual #físicos, #ingenieros, #matemáticos, #científicos, #programadores y sobre todo a los #estudiantes. Voy a incorporar esta forma explicarlo en mis técnicas didácticas para introducir en este tema. Reply @h2ogun26 8 years ago covariant vector.. im little confused when the value of dot products doubles along the doubling of basis' length, isnt the vector( white one. or V vector as you wrote) should expressed in basis which is before doubled? notice me if what my comment is imperceptible. 3 Reply 4 replies @AzmeenfilmsIndia 8 years ago I thank you for your noble deeds and efforts put into creating these. This deserves as many shares as possible. Reply @david21686 8 years ago Really? Einstein's field equations in the next video? You're going to skip over raising and lowering indices (which I really wanted to see), special relativity, curvature, the Riemann tensor, the stress energy tensor, and go straight into Einstein's field equation? 7 Reply Physics Videos by Eugene Khutoryansky · 3 replies @dremaro2967 1 year ago When the music is way to epic for the context Reply @ba_livernes 8 years ago Please, I beg you to stop moving things around so much when not necessary. It makes the video very hard to follow. 5 Reply @Daniel-dc5mr 8 years ago You should give the narrator a raise, she is great Reply @CasperBHansen 1 year ago Very distracting music 😅 62 Reply @hrperformance 6 months ago Thank you so much 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @chuckotto7021 8 years ago the music background is distracting and irrevelant 5 Reply @ClawHammermusic 8 years ago Such a tease! Can't wait for your intuition on the "Field Equations." Reply @kostaflex1994 3 years ago the music is distracting 17 Reply @mohammadmahmoody4657 8 years ago thanx alot you always focus on critical issues and help many people to understand in better way Reply @yuzhou5156 4 years ago That background music is annoying... 3 Reply @antonioalvarez3246 7 years ago Thank you!! A true hero for science :D 2 Reply @wurttmapper2200 8 years ago You returned! I was afraid it was a dream when I saw this notification. Your videos are fantastic. Reply @dnd3347 4 years ago Because Eugene named people are born wise. It is your wisdom that you create this visual representation of mathematics. Reply @paulbaker916 8 years ago So good to see you back. Superb as always. Reply @arnesaknussemm2427 7 years ago At last a simple illustration on the difference between co variant and contravariant components along with associated indexing. Brilliant. 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @jcfos6294 4 years ago Vraiment excellent. Un grand merci de France !!! Meilleur vidéo sur les tenseurs en langue française Reply @BooleanDisorder 1 year ago I have a tensor headache. 2 Reply @silvithomas 8 years ago No better explanation for a tensor has ever seen.Thank you Reply Physics Videos by Eugene Khutoryansky · 1 reply @bobbywasabi4082 8 years ago Thank you so much for doing the field equations I always wanted to learn about it! 1 Reply @bashirrather1562 2 years ago It is the most appropriate discription. Reply @blakewilliams1478 6 years ago Great video, first time I've ever gotten a straight answer about what a tensor is. Reply @dariuszbindacz8022 8 years ago I was thinking about covariant and contravariant vectors today and I also noticed email notification about this video today. Reply @ConceptsMadeEasyByAli 7 years ago This is so much better description and intuitive. God bless. Reply @shwetasharma5848 5 years ago Thankyou! Now I can see the imagination of those great personalities who discovered these concepts 2 Reply @Downlead 8 years ago Yeach... Finally Eugene releases a video about Tensor. I've waited for this video. Reply @harleyspeedthrust4013 6 years ago This is cool. I didn't realize it but tensors are used in backpropagation. When you multiply the activation vector for a layer with the derivative vector of the error over the net inputs to the layer, you get a tensor with the derivative of the error with respect to each weight (using tensor product as described in the video). This tensor is then used to train the network. I am glad I found this video because I knew what I needed to solve this problem, but I didn't know it was actually a tensor 1 Reply @nolongerjuicyboiz4413 5 years ago The sad music is very appropriate. 1 Reply @josephmazor725 3 years ago Thank you for the description of tensors, it’s one of the most intuitive I’ve seen Reply Physics Videos by Eugene Khutoryansky · 1 reply @PenguinMaths 6 years ago this music has me on the edge of my seat, like this symphony has strong feelings about vectors 1 Reply 1 reply @mermaid6380 6 years ago I like it a lot for the "slow" speed. It made the concept more understandable. Thanks! Reply Physics Videos by Eugene Khutoryansky · 1 reply @william22426 4 years ago gracias señora EUGENIA ,,SALUDOS DESDE COLOMBIA RESISTE SOS. Reply @sergiourquijo4000 8 years ago I just cant understand who gives a dislike and why? These videos are gold for anyone trying to study math in an intuitive way Reply @abhishekshah11 8 years ago CAN'T WAIT FOR THE NEXT VIDEO Reply @angeldude101 4 years ago This is the first video I've seen that's tried to show tensors visually and it helps a lot. This video: take every combination of components from a certain number of vectors and throw them in a supermatrix. Next video: General Relativity. Forgive me for saying this, but that is not what I expected to see for a part 2. Reply @gn2777 2 years ago This video is a precious resource for novices at tensor calculus Reply Physics Videos by Eugene Khutoryansky · 1 reply @geoffreyraleigh1674 3 years ago Thank you so much for making things simple and easy to understand. Reply Physics Videos by Eugene Khutoryansky · 1 reply @gibsonman507 6 years ago The William Tell Overture was hilarious Reply @kjenks2 7 years ago A very clear explanation of tensors. Nice, simple graphics. Reply Physics Videos by Eugene Khutoryansky · 1 reply @cristhianluque2748 8 years ago This is how all videos about mathematics should be :) Reply @rodrigoappendino 8 years ago I can't wait for the next video Reply @dalvikus 8 years ago Incredible video. Never saw a better visualisation of tensor than this one. Reply Physics Videos by Eugene Khutoryansky · 1 reply @Ingenieriaenyoutube 1 year ago Great video!🎉🎉🎉 Greetings! 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @srushtisonavane 6 years ago Excellent explanation to Tensors, your animation is on completely different level n so is your explanation. This video really helped me to clear my all doubts regarding tensors. I simply loved it. Thank you so much :) 2 Reply Physics Videos by Eugene Khutoryansky · 1 reply @kabelgeister 8 years ago (edited) This also makes perfectly clear why for a orthonormal basis the co- and contravariant components of a vector are identical. Reply @nazimuddin8459 4 years ago Very very helpful for any students studying in bsc(hons)... Reply @HidrogenoyMau 8 years ago Awesome summer recap Reply @yousufnazir8141 3 years ago Best explanation of the covariant and the contravariant in the form of covering the linear algebra and the geometry Reply Physics Videos by Eugene Khutoryansky · 1 reply @sdmartens22 8 years ago Great content! I didn't realize the dot product description was covariant. Reply @chenyang_wu 1 year ago It has been six years, and this video is still the best video on explaining tensor!❤❤❤ Reply Physics Videos by Eugene Khutoryansky · 1 reply @vwij1736 5 years ago A presentation with great clarity. Thank you. Reply Physics Videos by Eugene Khutoryansky · 1 reply @JohnVKaravitis 4 years ago (edited) 2:12 YES! FINALLY! The definition of contravariance! 3:31 And for co-variance. Reply @davidwright8432 8 years ago So THAT'S what covariant and contravarient mean!! I'd kind of just being batting symbols around, before. But now I know! Very many thanks, Eugene! I look forward to the next episode. the Actual Field Equations! Reply @mamneo2 8 years ago Thanks mate, I had troubles understanding this thing in class Reply @oscarlam5381 8 years ago I look forward for the next video. When will you finish your next video. The animation you made always let me have a deeper understanading Reply @sarutobihokage7488 6 years ago Thank you for this instructional video! I'm currently studying transport phenomena (momentum, mass and heat) 1 Reply @MohamedAli-xn3lk 8 years ago As all videos you did before ,all of them are great. this motivates me to create a youtube channel and trying to express and present your videos into arabic to be easy for Arab students to touch , see , feel and understand the science Reply @winniephy6 6 years ago Wonderful....! Just amazing.... Eugene... Your videos definitely make life easier for those who truely want to master physics and mathematical concepts.... Kudos for you efforts and pranams for the profound Knowledge that you are imparting through ur videos.! 1 Reply @TheGangstaman24 8 years ago so excited for the next video on einstein's field equations. I was desperately waiting for this on your channel. Reply @TheGamshid 8 years ago you are the best, Please don't stop. You are really making a difference. Reply Physics Videos by Eugene Khutoryansky · 1 reply @anamariaquintal2386 7 years ago Some times the discourse of the music colides with the speech of resoning. Here we have It. Reply @parthabanerjee1234 8 years ago Absolutely mind-boggling. Reply @donniedorko3336 6 years ago 8:23 You're kooky and I love it 1 Reply @robertengland8769 1 year ago This type of program appeals to my intelligent side. Thank you. Much appreciated. Reply Physics Videos by Eugene Khutoryansky · 1 reply @LoLStaticX 7 years ago One of the best math and physics channels out there! Reply Physics Videos by Eugene Khutoryansky · 1 reply @fernandoescobar4039 6 years ago Thank you for your service..! It is great help to understand these topics. Reply @thanosAIAS 8 years ago FINALLY!!! After many attempts to get what a tensor is, I finally GOT IT!!! Thanks, man!!! Now if only I knew what it's used for. I suspect it somehow measures the curvature of spacetime but in an independent way from the unit vectors of each observer. Reply @supergo1108 8 years ago Very interesting. I'm interested in the next part ;) Reply @mamar2313 6 months ago Lovely video, excellent explanation and superb music! Reply Physics Videos by Eugene Khutoryansky · 1 reply @yizhang7027 4 years ago After days of research, I can finally appreciate this video. Thank you very much for making it. Reply Physics Videos by Eugene Khutoryansky · 1 reply @hasanshirazi9535 7 years ago Great explanation of Co-variant and Contra-variant Tensors. Reply Physics Videos by Eugene Khutoryansky · 1 reply @sinant.1121 8 years ago Your math videos are always excellent !! Reply @varun3101 7 years ago this is most beautiful video i ever found on youtube.. huge respect for the team who made it Reply Physics Videos by Eugene Khutoryansky · 1 reply @markdevoges 4 years ago Jcrois jvais péter un clavier avec cte musique 1 Reply @armantavakoli7926 7 years ago Very nice explanations; I love them. Thanks a lot! Reply @jperez7893 10 months ago this is the best channel! thank you! Reply Physics Videos by Eugene Khutoryansky · 1 reply @margooka1963 8 years ago this was actually pretty helpful ty fam Reply @dabrownone 8 years ago OMG, I can't believe I've been trying to figure out tensors, covariant/contravariant components, etc for so long, and it suddenly made complete sense. great work! Reply Physics Videos by Eugene Khutoryansky · 1 reply @juanarcila5173 6 years ago Thanks for your video! I finally understood the difference!!! Reply @Kreyyn 8 years ago I'll be sure to check back here when I hit 3rd year physics! Thanks. Reply @cantkeepitin 5 years ago (edited) It takes Rossini‘s ouverture to know what a tensor is, but more than the whole Guilaume Tell to understand Einstein. Reply @amoghdasture2654 5 years ago This content is legendary Reply @depressedtm4701 7 years ago great explanation Reply @edoardoSM 6 years ago this video really helped me for my Relativistic Quantum Mechanics exam. Thank you 1 Reply @away5534 8 years ago I only have basic linear algebra notions, and I could understand it all, amazing explanation Reply @TheLonelyTraveler142 8 years ago I've been looking for so long for a nice explanation of what a tensor is. You really are the best at explaining physics and math, thank you. 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @nigeldupaigel 7 years ago The music is well matched. Thank you Reply @Alex4LP 6 years ago Great Music, great Math. The best possible combination. Reply @AbhishekKumar-yv6ih 6 years ago Animation speaks louder than words. Reply @stephenmenhennett6134 4 years ago wow what a great video epiphany at 8.05 Reply @timharris72 8 years ago This is the best explanation of tensors I have seen so far. Thanks for posting. Reply Physics Videos by Eugene Khutoryansky · 1 reply @DrBwts 8 years ago (edited) thanks for the clear explaination, I've been wondering for ages what the terminology actually meant Reply @AbuSayed-er9vs 8 years ago Great great.... explanation.And please make some video on geometric algebra,exterior product etc in coming future. Reply @michaelmontana251 4 years ago The music is crazy making Reply @ShammilAl-Abyad 8 years ago The dream is real! Thank you so much! Reply @zorro20010 6 years ago This is the most intuitive way to understand tensors for beginners i hav found Understanding Tensors has to b done togethr with concepts of covariance and contravariance Thanks Keep up the good work 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @DrakeLarson-js9px 1 year ago great video... teaching the viewers 'tensor language' Reply Physics Videos by Eugene Khutoryansky · 1 reply @dgm5208 1 year ago Love the music! Reply @charlesmcmillion5118 6 years ago Stand by for your vector, Victor. Reply @sashankvsl2202 3 months ago Greatest vid to start on tensors no doubt... Watching this for the nth time now but always had this question... What's with the music?? Quite a dramatic composition for something as dramatic as tensors!! Reply @luiservela 8 years ago I came with extremely low expectations to this video. I was positively surprised. Reply @muhammadsamisiddiqui2484 8 years ago Good work, still not clear, but didn't see that much simplification! Keep it up! Reply @GiladSofer 8 years ago Thank you for the video. Perhaps you could make another video sometime that explains (other than how tensors are constructed) what tensors represent and what they're used for (other than GR). Thanks again! Reply @williamwall1785 4 years ago I do like these videos; they explain concepts very well... for the most part. One exception to that here is that how the contravariant components of the grey vector are determined (near the video's beginning). That wasn't explained. So, I had to think about it a while, but I'll take a stab at it. To find the value of the yellow component, you form a vector from the projection of yellow onto the cross-product of red and green. Then projecting the grey vector onto that gives the number of yellows. To get the number of greens, you use the same approach with the yellow and red cross-product. Then the number of reds follows the same procedure with the cross-product of the yellow and green. The thought of doing this in higher dimensions makes me shudder. 1 Reply @alikarimi-langroodi5402 3 years ago Excellant. Thank you Reply @JaumeGarrigaTorres 2 years ago The music is good 1 Reply @satyapriyadas5486 4 years ago Wow !! Great video 🥰🥰 It cleared my concept way better than any other video or paper. Thanks ❤️❤️😍😍 Reply @burningoyster 8 years ago Damn that coming soon tease Reply @zorro20010 3 years ago Yet to fully comprehend it but I can appreciate th articulate xplanation Reply @rickandelon9374 8 years ago I am waiting for learning EFE so much plz make it happen thanks!! Notifications turned on !!!!!!!!! Reply @cemlynwaters5457 6 years ago The background music is sooooo sooothing :D Reply @naga540 8 years ago Please do Tensor Algebra, along with how to transform a co-variant component to a contra-variant one! Reply @edelcorrallira 8 years ago Beautiful, such a great topic served with clarity and with great music in the background that was expertly timed. I love how the introduction of the covariant vector is joined by a very intense and vigorous passage that later resolves to calm once explained. Delightful ! Reply Physics Videos by Eugene Khutoryansky · 1 reply @hochan7853 1 year ago (edited) OMG!!! This video explained some things that I have struggled with for years, despite reading so many things on tensors. Wow. Thank you. The Rossini background music is very appropriate. Reply Physics Videos by Eugene Khutoryansky · 1 reply @Jacob011 7 years ago This is awesome! I FINALLY understand all that co-variant and contra-variant business. I've never seen it explained so well. Reply Physics Videos by Eugene Khutoryansky · 1 reply @parjohansson3118 8 years ago An astonishing visualization of contra- and co-variant components! These videos should be used in physics lectures!! Reply Physics Videos by Eugene Khutoryansky · 1 reply @MrJesuswebes 8 years ago Wonderful video. Thanks for your job. Reply @FareedNagy 1 year ago a friend pointed me to this, this is so digestible for someone without a mathematics background. Reply @nekdozahadny4846 2 years ago We started learning about tensors about month ago... Since then I was completely list... This video has given me a hope to catch up again! Seriously great animation interperation as always :D Reply Physics Videos by Eugene Khutoryansky · 1 reply @AlwinKristen 8 years ago Great! Finaly an easy to understand video about the tensors Reply Physics Videos by Eugene Khutoryansky · 1 reply @m33LLS 7 years ago Great video! Could you do a video about stress (or strain) tensors? Reply @christianschmidt3171 6 years ago I've had covariant und contravariant tensors in a couple of lectures, but for some reason I missed the interpretation of what covariant and contravariant actually means. Thanks for this great visual explanation. Reply @innertuber4049 5 years ago These videos have helped me get excited about my major (Biophysics) again! Thank you so much! 1 Reply 2 replies @gpcrawford8353 8 years ago I'm not a mathematician nor have any qualifications but an avid interest in science since school days so when I read that Newtons theory ,instilled in me in my school days,was wrong I tried to understand it. Alas tensors came up this is the clearest explanation I have seen . From these superb series of explanations I have discovered that Acceleration produces time dilation and that is a major factor in Einstein's theory not the warping of space . Reply @Physicsnerd1 7 years ago (edited) Excellent Eugene. Great explanation and visual of co-variant, contra-variant, and sub/super scripts. Nice to grasp the concepts and rules of the game. I have had two different physics instructors who couldn't explain what you have put so succinctly. I have also read many texts that convoluted such simple material. I look forward to watching more of your videos. Thank you so very much! 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @jonni2734 5 years ago Awesome video!!! 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @nageshkothawale3533 7 years ago Animation is the very effective platform to visualise the mathamatics..and this channel is very good to doing that. Reply Physics Videos by Eugene Khutoryansky · 1 reply @wdew1927 4 years ago Very good explanation of the difference between covariant en contravariant tensors with beautiful simulation Reply Physics Videos by Eugene Khutoryansky · 1 reply @ctroy38 5 years ago Finally somebody clearly explains the subject... Reply @yamansanghavi 8 years ago This channel should be a standard thing to be studied in colleges and universities. Reply Physics Videos by Eugene Khutoryansky · 1 reply @-TOMORROW- 4 years ago すごく分かりやすい！！！！！！！！ Reply @BoIoko 8 years ago Another very good video as always ! Reply Physics Videos by Eugene Khutoryansky · 1 reply @MohamedAli-xn3lk 8 years ago As all videos you did before ,all of them are great. this motivates me to create a youtube channel and trying to express and present your videos into arabic to be easy for Arab students to touch , see , feel and understand the science Reply @ZombieSS77 8 years ago You are Richard Feynmaning many complex topics. I can't wait to see your EFE video. I spent 6 months studying enough math to learn the meaning of it last year, but I still struggle with the Christoffel Symbol. I hope you can clear that up in a video. Reply @supremegalacticcommander2783 8 years ago Pretty cool, but I will have to watch it again I think! I studied mechanical engineering in school and we learned about the stress tensor in elasticity, but this helps provide some deeper insight into tensors in their own right. Thank you! Reply @andrewkahn7345 6 years ago I FINALLY UNDERSTAND Reply @drashokkumar9209 2 years ago Superb presentation and graphics . Dot product has been always been a mystery to me . Reply Physics Videos by Eugene Khutoryansky · 1 reply @HarrieHausenman 5 years ago I got sea-sick from all the turning. Reply @moe531 8 years ago My all support Thanks Reply @tristanjohnson5247 8 years ago I clicked pretty fast just now to get to this video. Jokes and memes aside. P.S. I love this channel to death Reply @strangeWaters 2 years ago In geometric algebra, you add another the rule that says T[i,i] = basis[i] dot basis[i], and then a whole bunch of interesting stuff falls out like complex numbers and quaternions Reply @Nailesh232 6 years ago Fantastic. Reply @grimsk 4 years ago 한글자막 달아주시는 분 너무 감사하네요. 다른 영상들도 부탁드립니다..! Reply @sidhantbarik3465 4 years ago So thankful for this video.🙏 Reply Physics Videos by Eugene Khutoryansky · 1 reply @manjistharoy 6 years ago It would be great if u could do video on graphical visualization on quotient rule and chain rule Reply @gabrielmachado146 6 years ago (edited) Awesome vid! But I confess that I've struggled to not fall asleep when the Looney Tunes background music started at 5:50... Reply @KurohiNeko 4 years ago Beautiful explanation. Thank you so much! Reply Physics Videos by Eugene Khutoryansky · 1 reply @ian-haggerty 7 years ago Yessss! Finally an explanation behind the terminology "covariant" and "contravariant". It's alien language like this that can really throw me off learning new topics in physics & math. MAHASIVE Props to you. Reply Physics Videos by Eugene Khutoryansky · 1 reply @dixshants1227 4 years ago This is amazing. I am so appreciative of all the work you have put into these animations!! Unbelievable stuff Reply Physics Videos by Eugene Khutoryansky · 1 reply @UnsanHame 8 years ago Great animations as always. Reply Physics Videos by Eugene Khutoryansky · 1 reply @linomilita 3 years ago Thanks. This video is very important for me. Reply Physics Videos by Eugene Khutoryansky · 1 reply @areebashamshad7652 6 years ago hatts off to ur mindset👏👏👏 Reply @AndreaCalaon73 7 years ago Excellent video! Many ignore the origin of the co- and contra- prefixes. May be a reference to the reciprocal basis would help visualizing even more the two dual representations of vectors in non orthogonal reference frames. Reply @ernestuz 8 years ago Very well explained, took me a while to figure it out at the university. Reply Physics Videos by Eugene Khutoryansky · 1 reply @Maha-pu2qk 6 years ago I just want to thank you so much for your work. Thank you so much Reply Physics Videos by Eugene Khutoryansky · 1 reply @shomikhan1333 1 year ago Amazing visualization........ Thanks a lot.. Reply Physics Videos by Eugene Khutoryansky · 1 reply @luareis3739 3 years ago Absolutely amazing! Thank you for this video, I'm a bachelor student in Physics and I'm just taking General Relativity, couldn't understand what actually is a tensor in class, that's why I came here. This video really helped a lot :) 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @NagendraKumar-nv2sq 5 years ago Thanks for explaining the topic in animation which helps understanding the physical significance of the Tensor. Reply Physics Videos by Eugene Khutoryansky · 1 reply @stanis083 7 years ago Your video sir/madam is f****g amazing! Reply @hrishikad1271 4 years ago brilliant video, wonderfully explained. thanks alot Reply Physics Videos by Eugene Khutoryansky · 1 reply @lawrencedoliveiro9104 5 years ago 9:31 Interesting to observe the patterns in the arrangements of the component indices. Consider L¹V¹P¹, and the three planes (parallel to the axes of the cube) intersecting that position. In each plane, the components adjacent to the opposite corner include all three values for the indices. Thus, in the horizontal plane, we have L³V¹P² and L²V¹P³, in one vertical plane we have L¹V²P³ and L¹V³P², and in the other vertical plane we have L³V²P¹ and L²V³P¹. Something similar is true for the three planes containing L³V³P³. As for L²V²P², since that is in the middle, the “opposite” components now lie along each diagonal. Reply @francescoscorsin357 4 years ago he video is just wonderful, please decrese the volume of the music in future video... it can be disturbing for someone Reply @harikrishnanchandramohan4209 7 years ago Please start a series on Deep Learning. Would be really helpful for aspiring AI engineers. It is after all the future of the industry. One more humble suggestion as your student. For the kind of clarity your videos have, this channel can fill in the gap in the learner’s needs in the research. One such gap is the complexity in understanding the research papers of interesting AI projects. If you could make videos explaining the latest innovative ideas available as research papers, it will be very helpful. Reply @SomeHeavensStation 1 year ago Great video, insane music Reply Physics Videos by Eugene Khutoryansky · 1 reply @TheyCallMeNewb 8 years ago Approbation and veneration, you assist us in looking less the fools we are. Reply @xiaoyuvax 4 years ago The BGM is enlightening, lol Reply @rumpfma 4 years ago Your videos are such a big help when studying physics. Thank you! Reply Physics Videos by Eugene Khutoryansky · 1 reply @peterchen2892 8 years ago Math never came easier than this. Reply @ramseses 8 years ago This was a good explanation. Reply Physics Videos by Eugene Khutoryansky · 1 reply @manarmahdy8631 5 years ago I have to thank the producers of this videos. You make it easy to understand. Also the interpreters of this. Especially the Arabian. You helped me. Thanks. Reply 1 reply @exxzxxe 8 years ago Another excellent animation- this time of a difficult and abstract topic. Thank you. Reply Physics Videos by Eugene Khutoryansky · 1 reply @mendonka4612 4 years ago GRACIAS MUCHAS GRACIAS, LO ENTENDI :D Reply @khhnator 6 years ago remember that even Einsten had problems getting this Reply @ArpanD 6 years ago Forever changed the way i look at maths. THANKS AWFULLY EUGENE. U R DOING A MILLION DOLLAR JOB ACTUALLY U DESERVE BETTER. GO AHEAD SIR Reply Physics Videos by Eugene Khutoryansky · 1 reply @pendalink 7 years ago I watched this when it came out but now i actually need it for class, i love this channel! Reply Physics Videos by Eugene Khutoryansky · 1 reply @poppyflorist 4 years ago Before 3b1b, there was Eugene Reply @carloseduardonunez9543 7 years ago Clear explanation. Nice. Congratulations! Reply Physics Videos by Eugene Khutoryansky · 1 reply @Ecsenyi-Aron 7 years ago Very good video, thank you :) Reply @devrajyaguru2271 8 years ago This channel is awesome guys!!! Thanks for new content. Reply Physics Videos by Eugene Khutoryansky · 1 reply @maxholmes7884 6 years ago The 3D animations are what's really great about this video. Such things are necessary for a subject like Tensors in my opinion, and these 3D animations are very clean and accurate. Great job! Reply Physics Videos by Eugene Khutoryansky · 1 reply @ajmala1057 8 years ago awesome!!!! how u guys understanding these concepts this much clearly??? Reply @feynstein1004 8 years ago Amazing video, as always. I'm just so excited for the Einstein field equations. 1 Reply Physics Videos by Eugene Khutoryansky · 2 replies @erbenton07 7 years ago Eugene Khutoryansky: Can you do 2 videos - 1. on the vacuum energy and virtual particles (quantum foam) what are they, do they have charge? can energy be extracted from the particles? etc 2. on quantum entanglement 3. Bonus: How about one on 'dark flow' where it appears galaxies are moving towards a specific point in space. Your video's are very logical and easy to follow - excellent work! Reply @sandipjagtap1927 8 years ago Please make one video on finite element analysis......I urge this to you now....&doing it from 3 months....Please i think no one can explain it in a better way than u Reply @DougNeedham 5 years ago This is a great video, however I am having a little difficulty following. Can you show the steps to go from (4,2,6) to (1.826,5.055,3.567) ? I am trying to duplicate this in R, and I appear to be missing a step. Thank you, and keep up the great work! 1 Reply @marea_estelar 5 years ago How can you be so good at explaining complicated physics and mathematics??? You teach and induce passion for these subjects. Reply Physics Videos by Eugene Khutoryansky · 1 reply @sumanbagora277 6 years ago Thank you Reply @MosTech1 5 years ago Very nice ! Love the music too!! Reply @touristguy87 10 months ago (edited) here's an even better and much simpler explanation contra-variant tensors have orthogonal basis-vectors (equal amplitude, 90deg to the other basis vectors) covariant tensors have basis vectors that form a 90 deg angle with the tensor rank n is the # of columns -1 order is the # of rows --1 the tensor is indeterminate if m < n and it's overdetermined if m > n [An indeterminate tensor is a tensor that is neither positive definite nor negative definite. A square matrix is positive definite if pre-multiplying and post-multiplying it by the same vector always gives a positive number as a result, independently of how we choose the vector. An overdetermined tensor is a tensor that is part of an overdetermined system of polynomial equations.] it's a pseudo-tensor if it doesn't resolve to a vector in m dimensions. So a tensor in 3D space with time would be a set of position tensors (pages, levels, etc) Z (x,y,z,ti) where ti is the time-sample for that position Z(x,y,z,ti) any further questions refer to this video: https://www.youtube.com/watch?v=bpG3gqDM80w&list=PLfPLF9Z-SN7SVN4ZVfN0dyut7eKrGTaM0&index=11&t=20s&pp=gAQBiAQB Reply @Idkgoogleitbro 6 years ago The elbow grease behind relativity is difficult!, Conceptually I can understand as much as anyone else Reply @tensorbundle 4 years ago I have seen many brilliant professors in my PhD struggling to convey a concept. I do not know if you are an academician but I am sure that you have a bright-mind with profound insight in the topic. Your way of looking at things is so effortless and effective at the same time that it goes straight into the brain. Kudos 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @Everett-xe3eg 2 years ago The music is throwing me off. Thank you tho 1 Reply @frenchpet 8 years ago @8:30 the funniest most out of place music ever lol. Reply @realcygnus 8 years ago pure excellence as always !........can't wait for the Einstein equation vid......great stuff Reply Physics Videos by Eugene Khutoryansky · 1 reply @Лева-н4ч 5 years ago I’m really grateful!! And very good music) Reply @affablegiraffable 5 years ago What a good video. Thank you so much Reply Physics Videos by Eugene Khutoryansky · 1 reply @Surajalex1 3 years ago Great video nicely explained. Can you please suggest some books on tensors with same geometric visualization? Reply @rewtnode 7 years ago (edited) The oral explanations were very good. I realize though that I found the fancy graphics being of barely any use. The explanation of covariant versus contra variant was great. The graphics coming with that explanation however was mostly a distraction. However, when you letter explain 2nd and third order tensor I found the graphics quite useful. Reply @amydebuitleir 7 years ago Top=notch video! I did find the music a little distracting, though. Reply @rogerwilcoshirley2270 4 years ago Wow, very nicely done! Reply Physics Videos by Eugene Khutoryansky · 1 reply @alphonseraynaud976 5 years ago (edited) From a content point of view, which, in my opinion, is definitely the most important for educational videos, your videos, and especially this one, are great. The way you explained covariance and contra variance just tops everything I've stumbled upon in the last few months. What I liked about this video in particular is that you explain a bit slower than for example in the video about the Lagrangian? The only thing I do not love about your videos are the animations, but it's just from a pure aesthetic point of view (the vectors are too big, I prefer manim's way of representing 3D vectors, because I am aware that they work very well for teaching. edit: minor corrections Reply @FingerThatO 8 years ago Excellent. I have an exam just on this as you post. You must be a wizard or something. Reply Physics Videos by Eugene Khutoryansky · 1 reply @SuperSpinDr 8 years ago Awesome video and simple to understand narration. Thank you so much. OMG ! It took more than couple of decades for me to come across such a lucid and simple visual narrative that captures the essence of how a tensor is defined. This video is a vote in the plus column of why the internet and democratization of media such as this makes sense for mankind. Reply Physics Videos by Eugene Khutoryansky · 1 reply @venkatbabu186 6 years ago (edited) Tensors are mostly used in force balancing. Acceleration balancing and load balancing. Shortest distance calculations and shortest time calculations. Etc. Sometimes frequency control. Reply @randpaul9863 5 years ago Ouch, I think I just pulled a tensor Reply @carloschess2010 7 years ago What a great idea to explain as you do it. Thanks!!! Reply Physics Videos by Eugene Khutoryansky · 1 reply @classictutor 6 years ago Wow, you must have a God given talent for teaching. You've simplified it so that a high school student with a decent algebra 2 or a pre-calculus background would get it on a first go. Thank you very much! Reply Physics Videos by Eugene Khutoryansky · 1 reply @박준형-n6v 1 year ago 유튜브의 순기능👍👍👍👍👍 Reply @lanrelogan2468 8 years ago Love it Reply @Finne57 8 years ago Beautiful! Reply @quebuenavaina 3 years ago Excellent work. Reply Physics Videos by Eugene Khutoryansky · 1 reply @multimrhp3008 8 years ago Great as always. Reply Physics Videos by Eugene Khutoryansky · 1 reply @meruhere 5 years ago cool animation on the basis components! Reply @sciencepedia 4 years ago thanks for nice graphycal explaination Reply Physics Videos by Eugene Khutoryansky · 1 reply @sdsa007 3 years ago thanks for this, very important! impressive! Reply Physics Videos by Eugene Khutoryansky · 1 reply @emmanuelakeweje2349 4 years ago This is super awesome Reply Physics Videos by Eugene Khutoryansky · 1 reply @justanotherguy469 8 years ago Thank you so much for this video. It is so beautifully illustrated. I can not wait to watch the one on Einstein's Field Equations. Reply Physics Videos by Eugene Khutoryansky · 1 reply @Curt-f9o 2 months ago Great explanation! Love the music!...The William Tell Overture by Rossini! ❤😂 Reply Physics Videos by Eugene Khutoryansky · 1 reply @Luisitococinero 8 years ago This is fantastic! Reply Physics Videos by Eugene Khutoryansky · 1 reply @AJ-et3vf 3 years ago Awesome video! Thank you! Reply Physics Videos by Eugene Khutoryansky · 1 reply @HuggumsMcgehee 5 years ago This was very helpful. The way people talk about tensors makes you think that covariant and contravariant are two different classes that different vectors fall into. Like a velocity vector is contravariant, but an acceleration vector is covariant. This let me know that they're two different ways of describing the same thing. Reply Physics Videos by Eugene Khutoryansky · 1 reply @physnoct 7 years ago Good explanation of co/contravariant. I like how the music change with rank 3 tensors! Reply Physics Videos by Eugene Khutoryansky · 1 reply @osamamahmoud8921 3 years ago excellent simple explanation thanks a lot Reply Physics Videos by Eugene Khutoryansky · 1 reply @TheBrownHero 8 years ago I think I may have found the new Richard Fienman Reply @inevitablethor 7 years ago Brilliant channel Reply Physics Videos by Eugene Khutoryansky · 1 reply @bhanukatoch150 4 years ago Just outstanding Reply Physics Videos by Eugene Khutoryansky · 1 reply @jimlbeaver 8 years ago Great video, I was always hoping you would do the field equations...can't wait Reply Physics Videos by Eugene Khutoryansky · 1 reply @diegocadena7693 8 years ago Amazing work! Thanks for publishing it! Reply Physics Videos by Eugene Khutoryansky · 1 reply @seanki98 8 years ago very intuitively explained. amazing! Reply Physics Videos by Eugene Khutoryansky · 1 reply @장재욱-x5h 7 months ago you saved me. thank you! Reply Physics Videos by Eugene Khutoryansky · 1 reply @jptuser 8 years ago man you are great.. Reply @eangulozarate 8 years ago Thank you very much for your videos Reply Physics Videos by Eugene Khutoryansky · 1 reply @fisslewine1222 8 years ago You channel is amazing, great visual explanations, and puts far too many if not all university lecturers to shame! Would love to see a video on trigonometry and specifically in terms of graphics programming to create shape and collisions... Reply Physics Videos by Eugene Khutoryansky · 1 reply @lemmi0712 7 years ago This was really helpful.Thank you for uploading.😊 Reply Physics Videos by Eugene Khutoryansky · 1 reply @ludenhof 5 years ago Wonderful visualization! Thank you so much! Reply Physics Videos by Eugene Khutoryansky · 1 reply @bernardjacob3118 5 years ago (edited) 08:45 : Theorem of Bernie : Tensors of ranks "n" can be represented by a simple array (matrix) of dimension 2, with "n"^² colomn and "n"^² rows. (don't forget make the exponation to square if I understood correctly) Sometimes, when all students of our teachers are grouped in pub, we talk about our teacher and we call him as buckowski, Bernie the buckowski mathematician. Reply @IanFarias00 8 years ago Man, words can't express how thankful I am for that insight… I've been trying to get an intuition of this sort on tensors since I first tried to study them. Always been a fan of yours, now more than ever. Keep up with your excellent work! ^^ Reply Physics Videos by Eugene Khutoryansky · 2 replies @jamest.5001 8 years ago I think I missed something. oh no I didn't.. it just went over my head! great video I do think I missed something. Reply @yash1152 5 years ago (edited) 1:05 didnt know this way 👍👍 3:46 ohh now i understood this (i think, will be confirmed via practise) 9:58 u need to learn how to avoid death by 3d rotation (search for 'death by prezi', similar to 'death by powerpoint') (commented on 2019.12.29) i gotta say 'add to queue' is the best gift of youtube to me in the year 2019. loved it. gone are the days of 10s of tabs opened, only to lost track of what the heck i was thinking at the moment. It simply is amazing. Reply @ivana4638 5 years ago Thank you for the knowledge Reply Physics Videos by Eugene Khutoryansky · 1 reply @Dyslexic-Artist-Theory-on-Time 8 years ago Good info!!! Reply @VolksdeutscheSS 3 years ago This is a good channel and good explanation. One suggestion: I love music, but it doesn't belong here. It is distracting relative to the lesson. Reply @jithinpoliyedathmohanan7237 6 years ago Pretty cool viedio... 😎😎😎 Reply @darioromero4776 8 years ago Hi Eugene, your video about Tensors has helped me a lot. Amazing way to explain this complicated concept for me. However, my personal taste ... I'd prefer no music. It distract me a lot. Reply @unknown_russian_user 4 years ago Good video, thanks you for it. But i can't undestand one moment: why when we define a vector in basis vectors, then as the basis vectors increase, the result also increases? shouldn't he stay the same? 1 Reply @nandocova 8 years ago Thank you for another wonderful video! Reply Physics Videos by Eugene Khutoryansky · 1 reply @hariprasadoo 8 years ago Absolutely excellent tutorial 😊 Reply Physics Videos by Eugene Khutoryansky · 1 reply @MM-mc9ne 7 years ago Excellent video!! Reply Physics Videos by Eugene Khutoryansky · 1 reply @su_vigyatripathi9526 3 years ago Thank u million times🙏🙏❣️❣️ Reply Physics Videos by Eugene Khutoryansky · 1 reply @김연수-o9m1g 4 years ago 2학년 때 마리온 해석역학 솔루션 붙잡고 각각 두 번의 중간, 기말 공부 꾸역꾸역 했던 시간들이 허무해진다... 완전 헛공부했구나 나 Reply @viniciusfernandes2303 4 years ago Thanks for the video! Reply Physics Videos by Eugene Khutoryansky · 1 reply @brendanhall4590 8 years ago thank the maker!! Reply @quantumworld9434 4 years ago Now it is clear to me why the name contravariant and covariant vector. Reply @alejandromarulanda2325 5 years ago Wow How simple it is! Reply @seethroughlife1481 8 years ago This video helped so much. Thank you! Reply Physics Videos by Eugene Khutoryansky · 1 reply @ps49556n 8 years ago Awesome video. A suggestion: Choose colors wisely as it was very hard for me to distinguish between the green and yellow used in your 3D model (yes, I am color blind). Reply @lymanpaul4564 7 years ago very cool. great job! Reply Physics Videos by Eugene Khutoryansky · 1 reply @user-sf7qz5kg3b 6 years ago Intimidating Reply @rickandelon9374 8 years ago I was like waiting for this video for a whole year and today i finally got it i am now the happiest person in world can you plz make further videos of ricci tensor and manifolds i am in love with this channel ,Best regards from Nepal!!!!! Reply Physics Videos by Eugene Khutoryansky · 1 reply @apteropith 6 years ago I'm increasingly of the opinion that the directions (vector bases) and units (scalar bases) should always be explicit when dealing with vectors, bivectors, or any kind of tensor. It keeps things much cleaner and also helps elucidate that basis transformations are unitary: the vector before and after the "transformation" is itself unchanged, only rewritten, as basis transformations are but cleverly-arranged identity operations. Reply @supertren 8 years ago very nice explanation!!! :) Reply Physics Videos by Eugene Khutoryansky · 1 reply @EssensOrAccidens 7 years ago Appreciate the helpful instruction. Thank you. Reply Physics Videos by Eugene Khutoryansky · 1 reply @YuzuruA 8 years ago thanks Reply @gokulchandran5586 2 years ago Thank you very much. Reply Physics Videos by Eugene Khutoryansky · 1 reply @heardistance 8 years ago Very well explained ! Thank you ! Reply Physics Videos by Eugene Khutoryansky · 1 reply @andrewk2625 3 years ago Amazing! Thank you!! Reply Physics Videos by Eugene Khutoryansky · 1 reply @jlpsinde 5 years ago Great video! Reply Physics Videos by Eugene Khutoryansky · 1 reply @danielribastandeitnik9550 7 years ago Nice video, but the classical music was very odd... thank you very much!! 1 Reply @viratKohli-lf9pd 6 years ago Please make more n more videos,,👌👌👌👌👌👍👍👍👏👏 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @keycheeberlin 8 years ago I love your videos. Very good explainations. The only thing I find very distracting is your choice of the background music. You should go for ambient or downbeats, really ;-) Reply 9 months ago I don't know if I was learning math or entering war! Reply @SteveTaylorNZ 7 years ago I've zoned out, listening instead to the TROMBONES! Reply @badhbhchadh 6 years ago At 8:24 I had to laugh so hard! Reply @susmitabasak924 8 years ago thanks a lot... Reply @Kazami101 2 years ago Hi there, Enthusiast in general relativity here trying to teach it to myself. Loved your video. Why would we care about whether we describe an n-rank tensor in terms of the contravariant or covariant components of the vectors? Aren't they descriptions of the exact same thing? Many thanks. Reply @SahhiiChannel 4 years ago 何度聞いてもめっちゃ発音いいコナンくんにしか聞こえない笑笑 Reply @perdehurcu 1 year ago Muhteşem. Reply @trollfootballgeneration8645 7 years ago (edited) I love your vids Reply Physics Videos by Eugene Khutoryansky · 1 reply @RickySupriyadi 11 months ago (edited) why i always failed understand Tensor, but can understand vector since high-school i memorize the formula not the basus understanding because i still can't picture it in my mind Reply @khoanguyen5321 8 years ago Amazing! thank you so much 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @sujansharma9365 8 years ago amazed wow.... Reply @splat752 8 years ago Nice video. Looking forward to seeing the Einstein field equation video. Reply Physics Videos by Eugene Khutoryansky · 1 reply @stevec700 8 years ago Isn't this what Feynman used in Quantum Electrodynamics to describe how light that can take any path is resolved to one path? Reply @NhanNguyen-sy6kq 8 years ago This video is amazing!!! Thank you <3 Reply Physics Videos by Eugene Khutoryansky · 1 reply @muhseenmusthafa3769 6 years ago commenting to help you stand out further Reply @Maha-pu2qk 6 years ago I hope you do a video about affine connections Reply Physics Videos by Eugene Khutoryansky · 1 reply @aussiet5817 8 years ago Thanks. Reply @mooly15 8 years ago that was really helpful! thanks a lot !!! Reply Physics Videos by Eugene Khutoryansky · 1 reply @JackManhire 8 years ago These are great Reply Physics Videos by Eugene Khutoryansky · 1 reply @M0rb 6 years ago So if I got it right : - Fierce symphonic music - Dazzling effects and hypnotic swaying motions - Drowsy voice over are all contravarient components to the instructional vector of this video. 2 Reply 1 reply @thebhavyaahuja 3 months ago Great video but bgm was like im in jurassic park lol Reply @incredibalequang1812 3 years ago awesome, thank you ! Reply Physics Videos by Eugene Khutoryansky · 1 reply @AEvans853 8 years ago Great explanation video, but that background music - at least for me - is quite distracting... 1 Reply @GenericAspergian 8 years ago This is so good!!! Thank you!!!!!! Reply Physics Videos by Eugene Khutoryansky · 1 reply @carmelpule6954 8 years ago Congratulations for this video and the rest of the family of videos. Would the following breeding situation be related to tensors of some kind? Since within our universe, entities can exist in the form of points, straight lines, areas, and volumes and hyper-volumes, then one item may be looked upon as being made of particles which are located at various unique locations and orientations in the items in question. Let us say that particles that have their own particular characteristic can breed, transferring their own characteristic with "whom" they care to copulate or multiply. One condition is that they can only have one child at a time with one simple or complex partner, not twins nor triplets. Then, as breeding is a multiplication operator, the breeding can create new species with their own inherited characteristics. *So two isolated particles may be multiplied and the birth would cause a single product containing the characteristic of both parents. The result would not exactly be an area but it would contain more information that each of the isolated particles, at least retaining some indication of the location and orientation of the parent particles. * If one straight line is made up of many different particles, even if it is different location and orientation rather than substance which the particles carry with them, then, when all the particles in one straight line are made to breed or multiply by one other particle not contained in the straight line, then this breeding would create children where each particle in the straight line would be adulterated by the contents of information and what was contained in any two pairs that followed the breeding relation or multiplication. The product would be a wider straight line with new particles forms, which would be impregnated with the information contained in the pairs that bred them through multiplication. * If one straight line, made of different particles in different location and orientation is made to breed with other particles residing in another straight line wholly oriented in any other direction, then this breeding of particles would have to occupy an area where each particular born child would require a AREA housing for the complex products of the pairs that bred through multiplication process!. The housing area would contain different locations and orientations where each location would contain information related to all that was contained in both the parent particles! Taken as a whole this area of individual patches making up the total area would be very colourful indeed with all the new species bred through multiplication. The multiplication of two conventional three dimensional vectors would cause nine different children, as products, to be born. * If the area product of two vectors is now multiplied by a third straight line then a volume of different species would be created each having some relation to the three parents that sired them. For three conventional vectors the breeding would result in 27 different children each with a different DNA and that is not considering co and contra- variant possibilities! One can imagine the fraternity of individuals components that would be created if one multiplies ( a +b+c+d+e+f..)*(s+t+u+v+x+y+z..)*(m+n+o+p..) where all the DNA contained in each letter would be retained in each of the children bred through this multiplication. It would indeed be a Tense moment if this result decide to operate on something else in its vicinity. On reflecting back in my youth over 70 years ago, no one ever told me of what algebra did mean and it was such a pity that no teacher ever told me that if one associates a periodic delay information with any of the letter shown in this multiplication then (a+b+c+d+e+f)* (x+y+z+l+m+n+o+p...) then the product would represent all the input output relationship found in engineering! Or the convolution integral. Pity that most teachers do not illustrate clearly the real practical meaning and application of algebraic multiplication. I can cry for the many people who were not shown the wonderful music that algebraic operation does play in many fields of life. Reply @HolyManta 5 years ago Amazingly clear! Reply @juliangalindo3440 6 years ago I am amazed of how physicist and mathematicians define tensors or tensor fields so different and how in practice, they are the same. I dont know how to say it but the physicist definition is so "physicist" 🤣 1 Reply @vimal8783 1 year ago This music is from bomb squad game? 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @iTsEmS 6 years ago Its so awesome!!!! Thank you very much!! Reply Physics Videos by Eugene Khutoryansky · 1 reply @mjb4297 7 years ago (edited) Great video - just for future videos keep in mind that sound//music is contra productive to some types of learners - like me. VERY distracting. And I like the music ;-) Reply @visceralconfidence2987 3 years ago Wow, I have been totally enlightened. Thank you. In my quantum mechanics book (griffiths-schroetter) there is a part where a tenor like thing called a spinor Is brought up and used. I didn’t understand, but now, I wonder Just as how a Vector can be said to be a Matrix applied to the basis vectors Could an Operator be said to be a Tensor applied to basis operators? Like, taking the derivate or Taking the integral, are operators. They change the function given to them, into a different function. Hmmm.... Reply @davehumphreys1725 8 years ago Another excellent animation, but, the question that has plagued me for many years regarding tensors, was not explained. The opening sentence of the video contains that question. 'Tensors are mathematical objects that transform in a special way when the basis vectors change'. The one question I've never been able to get an answer to is why do you NEED to 'transform' these objects or 'change their basis vectors' in the first place? Reply @frankbholle 7 years ago Dear Eugene, you are truly a great teacher! I'm spreading your channel to all the people who like me are interested in these topics.I wanted to ask: are you planning to make a video about the quaternions? It would be great to finally have a clear one like what you did for the tensors. Thanks for all your work Reply Physics Videos by Eugene Khutoryansky · 1 reply @elnabjelland-hughes8172 4 years ago Very interesting video 👍😊💕 Reply Physics Videos by Eugene Khutoryansky · 1 reply @kateorman 4 years ago Spike Jones has destroyed the William Tell Overture for me. Reply @Yourstrulybong 8 years ago Great video👍 Reply Physics Videos by Eugene Khutoryansky · 1 reply @jayarava 7 years ago At 5:05 "Suppose we multiply one of the contra-variant of V with one of the contra-variants of P". It's not clear why we would do this or what it achieves. Reply @ericerpelding686 3 years ago Excellent! Reply Physics Videos by Eugene Khutoryansky · 1 reply @M6BrokeMe 7 years ago That was some of the most intense mental masturbation I have experienced in a very long time. Thanks! Reply @TheGuggo 7 years ago @Origami and pubs Kk I am also a pianist, Modest player though but crazy enough to venture into the Pathetique, the Moonlight and the Tempest. All them very demanding. Congratulations to you if you can tame LvB’s passion on the piano with any of his sonata’s. However the Pastorale fits better this video. Reply @kmmertes 5 years ago The content is very detailed and has clear definitions and descriptions. However, the music is very distracting. I have to focus harder to block it out. Would be better if the volume of the background music is reduced or eliminated. Reply @nightstar1759 8 years ago لقد هرمت من اجل هدي لحظه good job Reply @Ryan-wx8of 8 years ago Awesome explanation as usual, nothing to say really, just trying to boost visibility. Reply Physics Videos by Eugene Khutoryansky · 1 reply @plasmaballin 7 years ago 8:00 I think you mean "every possible permutation". Reply @esmam123 2 years ago (edited) Content is excellent. The background music is distracting. Reply @teddywhy12345 8 years ago Great video, thank you! Reply Physics Videos by Eugene Khutoryansky · 1 reply @ramchandradevkota9501 2 years ago Much helpful Reply Physics Videos by Eugene Khutoryansky · 1 reply @taarchi 8 years ago liàngWaaaauw, wonderful, been looking for such an explenation a long time! Great video! 看到你的关于张量的视频我非常高兴，现在明白了张量。非常感谢你！ Reply Physics Videos by Eugene Khutoryansky · 1 reply @solveigvan808 7 years ago Oh this was the INTUITIVE explanation. Well, shit. Looks like I need a lot of catching up to do. I'm out of my depth... for now. Reply @parmarthatkashi 8 years ago you are brilliant! Thank you! Reply Physics Videos by Eugene Khutoryansky · 1 reply @ahsnsb 8 years ago awesome Reply @EmMabuel5 8 years ago I would like to contribute with your videos, it would be interesting to do one on the Laplace transforms. What simulator do you use? Reply @clingurar25 7 years ago a tensor of rank one is a vector. got it. just like in thumb down the vector points downward. Reply @t3db0t97 8 years ago This is great! I'd really love an overview of what the role of tensors is in general relativity—i.e., we tensors are necessary. Thanks as always! 1 Reply @netastanciulescu5223 3 years ago Grazie Reply @omarhayat6016 6 years ago This is amazing. Reply @j.j.4708 6 years ago Are covariant vectors row vectors & contravariant vectors line vectors? (I read that somewhere and it makes sense when you're writing scalar & dyadic product with them, but not when you have a contravariant position 4-vector in special relativity to the RIGHT of a 4x4 lorentz transform matrix?) Why do covariant 4-vectors have a minus to their space components? (is is just so that s^2 which is the scalar product of the position 4-vector in co- & contravariant form can be written as (ct)^2 - x^2 ?) If you're taking the dot product of a vector with one of the basis vectors you'd get the projection of your vector onto that basis vector (component of vector that is parallel to basis vector), but wouldn't that be exactly the same as "how many of this basis vector we have to put together to produce our vector"? 1 Reply @roman_roman_roman 2 years ago Эта музыка на фоне дико неуместна 1 Reply @seriousmax 6 years ago "What makes a tensor a tensor is that when the basis vectors change, the components of the tensor would change in the same manner as they would in one of these objects." -- What objects? 2 Reply 1 reply @luiswolley3320 6 years ago "Simply Wonderful" Reply Physics Videos by Eugene Khutoryansky · 1 reply @stellank450 5 years ago This video took me forward as I am a man who need to see things whereever it is possible. As a K9 math teacher I had good use of my drawing habilities. I included some screenshots from this video in my tensor page at http://www.kinberg.net/wordpress/stellan/tensors/#visualized I hope it is ok. Of course I link back here. It would have been terrific to have your videos in my teaching. But I retired 2017. :) Have good day. Reply @buttyake_maru2 5 years ago アインシュタインの一般相対性理論に使われる数学ですね。 1 Reply @ZahraZobydii 6 years ago Wow, i realy like your video🥺great job. Reply Physics Videos by Eugene Khutoryansky · 1 reply @blueeyedpanda5051 5 years ago thanks so much Reply @saitaro 8 years ago Quality. Reply @あおん-q3s 1 year ago この動画は反変ベクトルだけでテンソルを説明出来るはずなのに、無理に共変ベクトルの説明も入れている（双対空間の存在を隠しているという意味）ことで逆に混乱する部分もありそう。とは言っても分かりやすくはある。 Reply @inboxsureshgn 3 years ago Thank you Reply Physics Videos by Eugene Khutoryansky · 1 reply @pmfara93 5 years ago Esto es maravilloso , solamente gracias Reply @stevolukic 8 years ago You are doing god's work. I will write this comment just to promote this channel. Reply to make this channel famous. Reply Physics Videos by Eugene Khutoryansky · 1 reply @adamhendry945 4 years ago (edited) I also wish the author would introduce the more modern terms for co- and contravariant vectors: tangent basis/vector = contravariant basis/vector, dual basis/vector = covariant basis/vector. Per Schutz (A First Course in General Relativity, pg. 60, Cambridge University Press.): "Most of these names are old-fashioned; ‘vectors’ and ‘dual vectors’ or ‘one-forms’ are the modern names. The reason that ‘co’ and ‘contra’ have been abandoned is that they mix up two very different things: the transformation of a basis is the expression of new vectors in terms of old ones; the transformation of components is the expression of the same object in terms of the new basis." So this video does a great job explaining the second part (describing an old vector in terms of a new basis), but the analogy is lost when trying to explain what a co- and contravariant basis vector is. Reply @vikrantvijit1436 5 years ago Excellent visual analytics appse art presentation, representation and creative visualization of complex mathematical information processing in Quantum Computing Universe Fabric interweaving forces of timing spacing fields effects resulting forms . Reply @stekenxu 6 years ago Very good video that explains these concepts! However, I want to mention a few things. Does the covariance as used here have anything to do with statistical covariance? From what I can see a covariance matrix is similar in form to the covariance of a rank 2 tensor, but I don't know enough about either topic to determine whether that resemblance is superficial. Also, could you not make the parts that are just the letters with subscripts sway? Reply @shickakaper8028 5 years ago This is like one of those rooms you go to when you die, but you don't your dead yet, then it starts to dawn on you.. "Where the f am I?.. Field tensors? Did i just drive through a guard rail? What is god? Is god a field tensor?" Reply @alejrandom6592 4 years ago (edited) Your videos feel like DXM Reply @lawrencedoliveiro9104 5 years ago 5:00 Hey, they look raytraced, with inter-object reflections. I thought this was all being done with a game engine. ;) Reply @raghuchar2347 6 years ago Excellent!, except for the music , a less strident & more mellow piece would suit, thank you Reply @AdrianBoyko 1 year ago Count Floyd’s 3D House of Tensors Reply @physlearner6458 2 years ago The explanations are good, but I find the music to be extremely distracting. It forces its way in, making me to pay attention to two things at once, which I can't do. This is especially frustrating when the music crescendos. I try to ignore it, but it's difficult because it's there demanding my attention. Again, this is especially the case when the tempo changes or when it crescendos. IMO, it would be better to leave it out. It adds nothing to the explanation. It may seem like a nice idea, but I don't think it works. After all: professors don't typically lecture with the radio playing in the background. 2 Reply @adithyapop2390 4 years ago Crazy Reply @jamgamber0 6 years ago Why the epic music? great video though 2 Reply 1 reply @davehumphreys1725 7 years ago Another excellent video! But, its not clear to me, when you create the matrices of the 'products' of the various components of the two vectors, whether the 'product' is a dot product or cross product. Also, no explanation is given as to WHY you would want to mix up the covariant and contravariant components of the vectors in that way. Lastly, what does the final matrix describe? Is it the addition of the two vectors, or the multiplication of them or what? Reply @alexander53 4 years ago But why though.... there is no "intuition" here. What's the point of doing this 1 Reply @robertaraujo347 6 years ago So, a tensor is invariant because it's constructed such that when a linear transformation is applied over his vectors, both change at same way and this produces the invariance? Reply @janniskoksel6336 4 years ago Vectors have never been that epic. Reply @philiptbs 8 years ago (edited) This in VR and some good acid mmh Reply @MathsatBondiBeach 7 years ago The distinction between covariant and contravariant components is frequently obscured. Indeed in the classic treatment of tensors that Einstein studied (Tullio Levi-Civita's works) it is all about linear transformations, Jacobians, Cramer's rule and so on so that the basic point made in this video gets lost. The point Eugene makes in this video is sort of made by some educators but not as clearly as this as far as I can recall. Well done ! Lot of work in those animations too. Reply Physics Videos by Eugene Khutoryansky · 1 reply @kunahariprasad5372 5 years ago Please make videos on senors ,and memory Reply @hi993114 7 years ago Thank you !! Reply Physics Videos by Eugene Khutoryansky · 1 reply @KeysToMaths 8 years ago (edited) It appears that if we double the lengths of the basis vectors from say 1 to 2, the length of V must be unchanged (say length = 10). What I found unclear was that the length of V would normally seem to be dependent on the length of the basis vectors i.e. if basis vectors were length 2 then V would have length 5 instead of 10. That must not be the case here, since doubling the basis vector lengths, doubles the dot products so value used for length of V is always 10 regardless of how basis vector lengths change. Getting double the value for the dot product must only come from doubling the value of the basis vector lengths. For the contravariant components, you are doubling the basis vector lengths from 1 to 2, but appear to be treating the new basis vectors as having length 1 (not 2) since the number of these basis vectors (not lengths) determine the components of V. Reply @lamalamalex 8 years ago :OOOOOOOOOOOOOOOOOOOOOOOO That's what tensors are?! Reply @yassinewaterlaw6597 2 years ago 0:42 why there is only 2 green basis vector the projection of the vector on the green basis vector span will be more than 2 green vectors Reply @Impatient_Ape 1 year ago The first part of this video on the difference between contravariant and covariant vector components is excellent!!! But when it gets to the tensor part, there may be some confusion. Due to the lack of standardization among the different scientific fields, it's common for the use of words "rank", "order", and "degree" for tensors to be conflated and confusing. What's called "rank" in this video actually refers to what mathematicians call "order" or "degree". The word "rank" is specifically used to count the minimun number of "simple" tensors we have to add up in linear combination to obtain a given tensor. "Simple" tensors are the ones referred to in this video. They are represented by K-dimensional arrays of numbers created from all possible products of the components of a set of K vectors. They have "order" or "degree" equal to K, but they only have rank-1. To demonstrate why, consider an NxN square matrix whose elements are deliberately created from all possible products of pairs of components from a specific pair of N-dimensional vectors. This matrix has order equal to 2. However, all of the rows/columns of such a matrix are just scalar multiples of each other. Consequently, the row space/column space has dimension = 1. Thinking of such a matrix as a linear map, since it's determinant is 0, it's not invertible; thus, it will not map the full N-dimensional vector space full onto itself. Since its "matrix rank" is 1, it will map the entire original N-dimensional vector space onto a 1-dimensional subspace. So using this matrix as a linear map, all vectors get mapped to new vectors which are along the same line. In engineering, data science, and and often in physics, the word "rank" is used when what is actually meant is "order" or "degree". In these contexts, just assume "order" or "degree" is what's meant when you hear the word "rank" being used. That said, quantum computing is a subfield of physics which uses the word "rank" as mathematicians do. Reply @naviddavanikabir 8 years ago What are the implications of tensors in Continuum mechanics or FEA? Anyone? Reply @atrumluminarium 8 years ago Maybe do a quick note on how to convert from covariant to contravariant (and vice versa) in the future please? It would help a lot Reply Physics Videos by Eugene Khutoryansky · 1 reply @mafuaqua 8 years ago Really a great channel! (sometimes sound is too low) Reply Physics Videos by Eugene Khutoryansky · 3 replies @josephhardin8391 8 years ago Thank you! Reply Physics Videos by Eugene Khutoryansky · 1 reply @hansbachmann8202 5 years ago A topografia do espaço tempo lembra, a topografia da Terra. O Alien Reply @Zack-xz1ph 7 years ago my brain hurts Reply @djehutisundaka7998 4 months ago Gμν = κTμν, Gμν + Λgμν = κTμνξ, κTμνξ is a 4 x 4 x 2 rank-3 tensor. Reply @davidgarrote6467 8 years ago At last! Reply @danielhirsen8753 3 years ago Beautifully explained, clear presentation on tensors. However, the well played rendition of wm tell overture is distracting. The beginning distracts by being beautiful. The mid portion has a difficult trombone solo, which reminds me how I couldn’t play it in high school. The third is triumphant, and does make one feel triumphant over tensors Reply @vinaydawar9247 5 years ago Beautifull Reply Physics Videos by Eugene Khutoryansky · 1 reply @thevegg3275 3 years ago Could you please explain mathematically how the g sub mn matrix if formed using ds^2=dr^2 + r^2 d (theta)^2 ? What was presented was g sub mn = [1 0, 0 r^2]. Note [1 0, 0 r^2] is a two by two matrix Reply @astropredo 8 years ago SUPERB! Reply Physics Videos by Eugene Khutoryansky · 2 replies @yuyo1948 7 years ago El video esta bien, mejor estaría con subtitulos en español Reply @fahraj1561 3 years ago Love you Reply Physics Videos by Eugene Khutoryansky · 1 reply @ashrafulislamkhan9936 3 years ago ❤️❤️❤️❤️ Reply @artiomlukin3187 8 years ago Amazing video! Could you please tell me what the music you used was? 1 Reply Physics Videos by Eugene Khutoryansky · 1 reply @txemaglez8251 1 year ago great!! Reply Physics Videos by Eugene Khutoryansky · 1 reply @timothytomkins 4 years ago Nice, but it would have been of real value to explain, from the very start, how tensors are fundamentally useful in the practical world because they enable associated data (eg position,direction, and speed of a group of snooker balls) to be efficiently ORGANISED, REFERRED to, and OPERATED (or CALCULATED) ON..For example given the positions of every snooker ball now, we try to predict these parameters a short time later...and tensor approach just helps us, organizationally speaking, in setting up and doing such calculations. Discussion of definitions such as "rank" ,"covariant","contravariant" etc, can be best discussed later when the student can fully understand that these are no more than fancy names of no real fundamental importance and ONLY THEN enjoy the introduction and use of these fancy names, knowing deep inside how they are very much secondary to the understanding of the subject! It is so useful for students to understand from the start that, fundamentally, tensors have no fundamental or special meaning in physics or finance or anywhere else- they ARE just a useful organizational approach, especially in the age of computer based algorithms such as neural networks. It would be nice to see what proportion of tensor users would agree with me on this learning approach.. Reply @ramashama-tw3ly 9 months ago 🙏🙏🙏 Reply @adiazdu 6 years ago Do you have any video about the Hilbert transformation? Reply @gonzalorizzo7239 5 months ago I still don’t understand tensors but thanks for trying Reply @ShaolinMonkster 5 years ago Hello , very good work . A good idea would be to give some real life examples Reply @fayazelahi 7 years ago l luv u very much Reply @이진호-o7x 5 years ago 이것은 무슨 알고리즘인가 ㄷㄷ Reply @rodrigoappendino 8 years ago (edited) What about spinors, used to describe fields in particle physics? Are some kind of tensor? Or tensors are some kind of spinors? Reply @travishohenberger7911 1 year ago Thank you for the video. Have you made a video to frame these concepts in terms of the stress tensor? I am struggling to figure out some aspects of the rank-2 tensor in mechanics. Reply Physics Videos by Eugene Khutoryansky · 1 reply @deusvult5738 5 years ago I've just learned about bilinear maps. So... there's a lot of confusion, but it's basically a multi-linear map right? The only problem is expressing it computationally (through basis vectors). Reply @errorusernamenotfound9013 7 years ago Anyone know how he got the values of 1.826, 5.055 and 3.567 for the dot products at 1:04? Is there enough information on the screen at 1:04 for us viewers to be able to calculate these values? I thought we would at least need to know the angles between each basis vector (red, green, yellow) and the white vector? Also, is the length (magnitude?) of the white vector = square root of (2^2 + 4^2 + 6^2) = square root of 56? Thanks to anyone who can help! Reply @finderscope5447 5 years ago 번역이 깔끔하네 Reply @ImPresSiveXD 6 years ago How to calculate the covariantvector from the contravariantvector? Reply @DGaryGrady 6 years ago Excellent video once I turned on captions and turned off the sound. The background music is too loud and if you left it out entirely I could listen to my own background music. Sorry to gripe -- I really liked the video itself; it was just frustrating to have someone else's music choice forced on me. Reply @procdalsinazev 8 years ago I am confused a bit. The space of pairs of 3-dimensional vectors has dimension 6 while the space of all 3x3 matrices has dimension 9. That means that either not every matrix represents a 2-dimensional tensor, or the tensors described represent just a very special type of tensors. I expect that the second option is right but what is tensor in general then? Reply @veal4 5 months ago Nice music Reply @ChristianGonzalezCapizzi 8 years ago What does it mean to multiply two unit vectors together? What's the operation being done? A dot product? Reply @curiousmaniac9495 8 years ago please make a video on transforms ( laplace, fourier, z transform ) as these will help many engineering students.Many people take it for granted very little is known about its physical meaning, there are subjects in engineering based on transforms like signals and systems, signal processing, control theory ,etc your videos will surely make a difference in understanding these subjects. Reply Physics Videos by Eugene Khutoryansky · 3 replies @tommy7788 7 years ago I just know that a vector can also be described using its dot product with the bases, but how do I show that such description will give a unique representation of that vector? Reply @denestandary3372 4 years ago Is there a video with the same content, but with a numerical example? Cd you recommend a book where such an example is elaborated? Reply @atimholt 5 years ago Do the covariant indices presuppose that absolute angles are a thing, or is it just the dot product in terms of the basis vectors (“as if” they were mutually orthogonal), or in terms of an arbitrary basis (as an optional 3rd consideration)? Reply @jorgeguzman6685 7 years ago If I describe vector in terms of dot product with each of basis vectors? Reply @oleolee4874 7 years ago Wow, awesome work. Very nice visualisation, congrats! I would even more appreciate such a great explanation for the Riemann tensor! Which programm are you using for the visualisations? Reply Physics Videos by Eugene Khutoryansky · 1 reply @none6986 1 year ago The music is really distracting otherwise 10/10 1 Reply @ravirajh6658 8 years ago 👌👌👌👌👍👍👍👍 Reply @admiralhyperspace0015 4 years ago have my comment for the algorithm. Reply @grantgibson8034 6 years ago Great video tutorial and a great piece of music from Beethoven but somehow the combination does not work well. Reply @Zayka007 1 year ago Can anyone explain to me why we have to do all this? I mean what's the objective behind it, is it just a method to multiple vectors in space ? Reply @bernardjacob3118 5 years ago 03:20 : In fact, this representation is just a representation by the scalar multiplication by vector with another vector. It's possible to represent that with a orthogonal projection of one vector on the second vector. On this website, you can simulate and have a better comprehension but, sorry, it is in French : https://www.cmath.fr/1ere/produitscalaire/cours.php And in fact, I call that representation as scalar vectors representation, and in fact, we can observe then if the basis vectors increase, so, the component of our main vector increase too ! It's the covariant indice ! and the mathematical convention likes to put those indices to bottom..... Reply @bingbongabinga2954 6 years ago All these line thingys are different for the observer vs the traveller at speed? Reply @Andrewl9110 8 years ago bump for the video (= never miss a video from you question: what makes you decide on what subject you will make a video each time? Reply Physics Videos by Eugene Khutoryansky · 1 reply @tiagotiagot 8 years ago So tensors are just a way to represent multiple vectors? Or do they got some special properties or behaviors? Reply @TheZenytram 8 years ago so a tensor is a cluster of vectors? Reply @abcdef2069 2 years ago i need examples, is it possible to solve a sphere's surface area with tensor or geodesic or something? Reply @SupremeCommander0 8 years ago Could you make a video about band gap, what is kt/ktmax (https://upload.wikimedia.org/wikipedia/commons/3/35/Cnt_zz_v3.gif), density of states, etc.? Reply @victoriavampa5857 2 years ago Excellent. It is not clear for me how the values 1.826, 3.567 and 5.055 are obtained. And in the case of covariants components if you duplicate the basis vectors, but they have to have length unity? Reply @Niharikajain72828 7 years ago abbabbbabbabbababbabbabababbabaaaa....!!!! Awesome video Reply @pelimies1818 4 years ago Why the need for all the combinations? Reply @ravishanker785 7 years ago Tensors for Beginners: https://www.youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG Reply @Andrew90046zero 4 years ago (edited) So if I write out a vector on a piece of paper, say: (3,7,5) Like so Is that covariant or contravariant? Or is there not enough information to tell? I would guess it matters more when you “have the arrow” but want to find the components of the arrow. If you have the components, and can just produce the arrow as normal. Reply @SlamDunkMunk 2 years ago Oss! Reply @zes3813 8 years ago aargh, you guys were fast to click on this. Reply @tanzanite423 8 years ago (edited) Is there any meaningful reason why the PIV has to keep changing? Reply @XinmiaoQiuGodiscarrot 3 months ago remarkable music lol Reply @ZioAlboz 8 years ago (edited) Why are there these 2 ways to describe a tensor, co-variant and counter-variant? What is the purpose of each one? Reply @ZweiZombies 7 years ago So every rank n tensor can be created from some combination of n rank 1 tensors? Reply @BarriosGroupie 6 years ago This can only have been made by a physics PhD with years of teaching experience. Reply @physnoct 6 years ago (edited) Expressed mathematically: Contravariant Sum of basis vectors a = (a/λ)(λ u ) + (b/λ)(λ v ) + (c/λ)(λ w ) Covariant Dot product with basis vectors λa = a ⋅ (λ u' ) λb = a ⋅ (λ v' ) λc = a ⋅ (λ w' ) Reply @somipark4990 5 years ago 양지영실내달력메모기도 Reply @shmeeps9605 6 years ago How's that used in life? Reply @adamhendry945 4 years ago (edited) This is a great video, but I only wish the author would emphasize that there is no distinction between co- and contravariant components for mutually orthogonal basis vectors (i.e. an orthonormal basis). Around 0:28, the author simply says "Let's pick new basis vectors". Co- and contravariant components differ when the basis vectors are not mutually orthogonal, but otherwise there's no difference. This is an area where people get easily tripped up. Reply @jzargowinterhold1942 8 years ago Tensors are tense Reply @marcofurlan2015 7 years ago Did you notice the cat at 9:10? Reply @perdehurcu 1 year ago Hello. Sir, okay, but what good will knowing these do us? We can easily describe axis transformations with gradient divergence or rotational functions. Our scales change automatically in coordinate transformations. We can profit from this right from the start. I don't understand why we need to use tensors. If anyone knows and can enlighten me, I would be very happy. Thanks. Reply @hqs9585 2 years ago What is meant by "Combination of Vectors or components of vectors"? product...?..? Reply @ankurkumar9660 4 years ago (edited) Eugene , some teachers teaches tensors as a transformation matrix . They say a 2nd rank tensor is a matrix . Is it true anyhow? Please answer me😊 Reply @hinakhalil5593 2 years ago 🎉 Reply @vishisbest 8 years ago 👍 Reply @CstriderNNS 6 years ago DURING THE EXP. OF ACOV & CONTRAVARIENT VECTORS, YOU COMPAIRED THE CONTRA VARIENT BASIS VECTOR TO THE UNCHANGED TENSOR, BUT YOU COMPARED THE COVARIENT VECTOR TO THE TENSOR TIMES 2 , WHY COMPARE LIKE THIS, WHAT IS THE "SYMMETRY " OF THES TENSORS ????(OPS CAPS LOCK LOL) Reply @Omkar_ओमकार 6 years ago So, tensors are only for contravarient vectors, aren't they? Reply @elir7184 4 years ago Eugene, Im not sure if youll see this but... i recently asked a question on quora wondering if a quantum state can exist in an infinite number of superpositional states, to which I recieved an answer saying that in quantum mechanics basis vectors are actually basis states. Do you have any videos that could help me with this? Reply @gyaneswarbhoi8798 5 years ago Good Reply @vanadium4603 4 years ago clockwork orange flashbacks Reply @bingbongabinga2954 6 years ago Time considered as a vector? Reply @catchylow3444 7 years ago The spinning diagram gave me motion sickness. Reply @CTimmerman 7 years ago So a tensor (always 3 dimensional?) has n ranks, where n is the number of vectors it combines? Reply @John77Doe 8 years ago A tensor of rank one is a vector. 😮😮😮😮 Reply @thevegg3275 2 years ago Hi, at time 3:42 you say another way to describe a vector is to take the dot product of the vector with each of the basis vectors. Given all the angles shown being 90 degrees and in accordance with the definition of the dot product...that would mean that all the scalar numbers you show should reall be 0.000, because the cos of 90 degrees is 0. I'd love to get this cleared up. Thanks! Reply Physics Videos by Eugene Khutoryansky · 1 reply @somipark4990 5 years ago 식당이용후성격이상해진환타 Reply @karabaskruger 5 years ago Только надо бы сказать что в случае ортонормированного базиса они совпадают. Иначе вызывает недоумение: это же одно и тоже , а почему разное? Reply @izetassky 7 years ago about 8:00 i am not sure understand it well, we have basis (5 yellow, 2 red, 3 green) so i can use T^11= (4 yellow, 1 red and 2 green), and (5 yellow, 0 red 0 green). what is the exact definition of "every possible combination of these two basis vector?? can you give some clear example of 2 rank tensor has same basis. Reply @周振國覺悟者 1 month ago 🎉 Reply @pinsonraphael4873 2 years ago I've never seen an explanation of tensors that I could understant, thank you! If the family of base vectors is orthonormal, does that mean that the covariant and contravariant components of the tensor in that base are the same? Since the coordinates of a vector V in such a base (e1, e2... en) are given by this should be the case but maybe i'm missing something Reply Physics Videos by Eugene Khutoryansky · 1 reply @terryphi 8 years ago Can you do some tensor applications? Reply Physics Videos by Eugene Khutoryansky · 1 reply @Fredgast6 8 years ago Could you please make a video about the p-n junction? Reply Physics Videos by Eugene Khutoryansky · 1 reply @carlosromerogarcia1769 3 years ago It' curios how is science, I'm here traying to understand my finance program done with Tensor Flow (A.I.) Reply @tahafahim5011 4 years ago what's is the program you use? 1 Reply Physics Videos by Eugene Khutoryansky · 2 replies @DoctorClarinet 6 years ago Hi - thanks, I really enjoyed this. Sounds like a great version of Rossini's William Tell Overature - what was the orchestra? Reply Physics Videos by Eugene Khutoryansky · 1 reply @CapemanProducti0ns 5 years ago And a tensor of rank 4.... is to go... even further BEYOND! Reply @umamaheswarareddy3418 6 years ago In this video,you said that a tensor of rank 3 is composed of 3 vectors. Could you pleassse explain what exactly the word "compose " mean? Is it a multiplication or addition or anything else? Reply @toddseiler 5 years ago Why would you mix / match contravariant and covariant descriptions to create a tensor? What does that even mean? Reply @simonvandenbroek6384 5 years ago (edited) Hey There eugene, I liked your video alot. could you provide us with a very simple, yet practical example on what it's been utilised for. what are the general uses for this matrix as opposed to the data we gather from the cross product or dot product of 2 vectors. simply put, why do we calculate the outerproduct as opposed to how. I am studying 3D procedural content generation and I'd like to just go a bit deeper with the math. Reply Physics Videos by Eugene Khutoryansky · 1 reply @somipark4990 5 years ago 최시내보다과부돌일때양지영 Reply @robertomarras9705 3 years ago Potresti dirmi come si passa dalle lunghezze 4:2:6 a quelle del prodotto scalare 1,826:5,055:3,567 ? Reply @andrewniven4350 6 years ago Sorry, I am a bit confused over the definition of the co-variant components - if the basis vectors are larger than 1, then the dot-product components, along each basis axis, seem to grow beyond the tip of the vector. How can they still represent the same vector? Also, would it be correct to say that as the basis vectors grow the contra-variant components shrink and the co-variant grow but their product remains the same? Thanks. Reply @정예지-e2p 3 years ago (edited) does verctor P has contravariant component which is covariant component of V, right? that explanation is omitted. Reply @shitongchai9403 7 years ago physics is likely to be closely related to math Reply @davidmelgarejo8751 8 years ago Hi Eugene, what your are doing is a fantastic aid to all interested in math and physics and in education in general. How can I contact you? Sent you a message by Linkedin Reply Physics Videos by Eugene Khutoryansky · 1 reply @poonampandey3655 5 years ago (edited) Ok ,so for the first time I want to pay for a YouTube video and maybe for the channel itself.😍 Reply Physics Videos by Eugene Khutoryansky · 1 reply @perdehurcu 1 year ago Hello. Sir, for example, if I take the size of the unit basis vectors as Plank units, can't I keep the number of components unchanged? Do unit basis vectors have to get longer and shorter? Thanks. Reply @AlbertoScocco 10 months ago Really effective.. thank you. Only an advice: the music is a little bit distractive... :-) Reply Physics Videos by Eugene Khutoryansky · 1 reply @cyrusdeng0108 1 year ago let me understand what is covariant and contavariant Reply @michaelmacdonald2907 8 years ago So, what is a tensor ?! Is it a resultant ? Is it a cross product ? A dot product ? Or is it just a matrix that describes the same 3 vectors in 27 different ways. Reply @bonbonpony 8 years ago Cool, you showed how to mix the numbers & stuff, but seriously though, what IS a tensor? There's still no answer to that question in this video, so nothing has been really "explained intuitively" :P Reply @kareszt 7 years ago 1 week - internal thought. Google provided. Reply @xyzme1217 2 years ago The constant rotation is dizzying Reply @hussienmohamed8766 8 years ago (edited) your videos are so interesting and make sense of the concepts of physics an mathematics but i have a question about this video you mentioned that we describe the vector by using the dot product of the vector and the basis vectors but we know that the dot product is a scalar quantity so how can i describe a vector quantity using a scalar one ? thanks Reply Physics Videos by Eugene Khutoryansky · 2 replies @iveharzing 2 years ago (edited) This is a very good explanation, but it has left me with even more questions: These contra-/covariant components of a vector are defined with respect to certain basis vectors. But then what are "contra-/covariant basis vectors"? (compared to "contravariant basis vectors") I assume the basis vectors used in this video are "covariant basis vectors"? How do I interpret "contravariant basis vectors"? Reply 1 reply @aymanghaibeh8589 9 months ago I wish you sped it up a little Reply @Kenbomp 6 years ago Why rotation? Getting dizzy Reply @킹반-w1m 5 years ago Great video! But I feel digestive disorders watching this bcz of the turning view. Reply @somipark4990 5 years ago 버섯인상극장 Reply @thomaslehner5605 7 years ago Good video but distracting music Reply @thevegg3275 7 years ago The problem with your nice video is where you increase the dot product to show covariance. Sure, the increase in length of the basis vectors increase the dot product BUT you have then entirely broken the connection whereby the dot product length projected perpendicularly to the tip of the vector actually projects to the tip. Following that logic, I could say the increasing basis vectors INCREASES the contravariant components as long as I'm not constrained to having the projection of the length reach the tip of vector. What am I missing, please. Reply @EmMabuel5 8 years ago Hi, what's the name of the program you use to simulate? greetings from Mexico Reply @somipark4990 5 years ago 2단계성형 Reply @volvlov759 8 years ago What program do you use to generate your graphics? Great graphics and explanations! Reply Physics Videos by Eugene Khutoryansky · 1 reply @Euquila 4 years ago But why have contravariant at all? Why not simply do all the work using covariant basis? Reply @kebabsharif9627 7 years ago Thank you very much for such a good leucture,Can you please tell me the name of the software that you used for making this video . Reply Physics Videos by Eugene Khutoryansky · 1 reply @rickmonarch4552 1 year ago Okay I understand this but I didn't get what it's good for to multiply covariant with contravariant or why would I even use covariant? Contravariant is way more intuitive. Reply @theonionpirate1076 5 years ago (edited) What makes a tensor a tensor is that when the basic vectors change, the components of the vector would change in the same manner as they would in one of these objects. Sorry, I don't understand the last part. One of what objects? And what do you mean by "in the same way"? It is this point that I keep not understanding in every video about tensors I watch... and seeing as it's the definition of a tensor, I'm still not seeing how a tensor is anything but a product of vectors. An example would be helpful, and perhaps a comparison to a pseudotensor to show what's different. What started me off is watching Science Asylum's video on tensors and trying to understand the part about how angular momentum is a pseudotensor because depending on the coordinate system, it's not always the same and can be 0. And then the whole 4-velocity thing... Reply @somipark4990 5 years ago 시내식당이용 Reply @yarazdolbai 3 years ago меня укачало Reply @sahiljindal9663 6 years ago Seriously what the hell where do you tell the basic meaning of tensor why and where do we use it Reply @baharjafarizadeh7806 7 years ago what the hell of the music! Reply @somipark4990 5 years ago 슬리퍼운동화 Reply @somipark4990 5 years ago 가운데졸업사진의자옥미 Reply @vpagl 8 years ago Amazing video! , one question though, at 2:54 "when you double the length of the basic vectors (green, yellow, red), it's associated dot product also double" that means resultant (white) also changed? If not, why? and if yes, white changed, then "co-variants" will give a different vector always. I am in a vector dilemma. 1 Reply Physics Videos by Eugene Khutoryansky · 3 replies @TonyRios 8 years ago Tensor Matrix Reply @absolutelynothingtoseehere 4 years ago The style of presentation is very good, but there still is no discussion of the physical significance of tensors, which is what I'd consider to be an "intuitive" explanation. This video needs to be part of a larger explanation. Reply @thevegg3275 5 years ago I'm studying Vectors and Tensors (Fleish). I read that vector components can be defined by paralell or perpendicular projection. Paralell projection components correctly add up to the original vector but perpendicular ones do not. My questionis if perpendicular ones do not up correctly, why is it a thing at all? It just makes us create the dual basis vector as a work around. I could additionally make up my own projection that would force me to create some workaround. Let's say we project at a 45 degree angle. I am sure I could create a method to make those components add up to the original vector. But why do any of this if paralell project works fine. Maybe we only need one? Reply @palantea1367 4 years ago what are you calling contravariant? :( both basis and components or just the components? Reply @ramingolbang2417 8 years ago The videos are magnificent, but what is the deal with the background music?! Reply @GorilaMaguila 7 years ago Great video but Rossini's music is very nice but does not help to stay concentrated. Reply @hhhults 6 years ago + Reply @somipark4990 5 years ago 허은주 앨범안버렸다 Reply @seymourknecht1232 8 months ago The background music is really distracting Reply @merbst 6 years ago Funny music. Reply @beria6838 3 weeks ago <3 Reply @JeffSCHLPN 8 years ago (edited) How do the two methods for finding the co/contravariant components yield different results? Surely the dot product of a vector with a basis vector equals the amount of that basis vector contained in the vector...? I would think the two values are equal. Reply Physics Videos by Eugene Khutoryansky · 1 reply @andrewens3337 2 years ago Is this video implying that covectors and vectors are the same object, just represented differently? In tensor algebra contexts I've seen the covector also represented as a function that takes vector inputs, but vectors stayed as just vectors. 1 Reply 1 reply @yogran1 7 years ago If you increase the basis vectors and the dot product increases ie the length of the lines are increasing then won't the vector itself also get bigger? Reply Physics Videos by Eugene Khutoryansky · 1 reply @francisbacon4363 4 years ago 8:33 Reply @mehershrishtinigam5449 2 years ago i feel like throwing up this video is making me so queasy Reply @dilanramoscalizayaelt4378 5 years ago 👍👏😀 Reply @pierluigidesimone6971 7 years ago my bit: better no music, it is distracting. Also no need to introduce the need of a base change to explain contra-variance. If you double the unit length then vector coordinated will half. This hold true also in the Cartesian coordinate system. Thank you Reply @rayfletcher8759 6 years ago What if you had 4 basis vectors? What would that do to the matrix? Reply 1 reply @tk-gf7dw 5 years ago 曲のチョイスがホント謎 Reply @muzammalsafdar1 8 years ago can you completely explain tensors? it may take lot of time. please can you tell me that which literature you use to make your videos? Reply @albertovalsania8656 6 years ago Is possibile ti Gent ITALIAN subtitles? Reply @odeo3550 8 years ago I comment this just to add more comments Reply Physics Videos by Eugene Khutoryansky · 1 reply @somipark4990 5 years ago 어떤 미옥의 긴치마 Reply @adityamishra858 5 years ago (edited) Hey everyone, how one can get the components of covariant vectors given that contravariant conponents. Thanks in advance, Reply 1 reply @edithseichter4857 5 years ago Great videos. Im still not truely understanding it. Im missing something. Reply @kunx5387 3 years ago Can someone explain the lengths from the dot products? 2:54 Reply Physics Videos by Eugene Khutoryansky · Replies @ppugalia6492 6 years ago Where are Adam and Sarah ? Reply @somipark4990 5 years ago 오븐수제빵사진꼭페이스뿍 Reply @jasonruzicka7954 1 year ago 8:22 Take the ride of your life Reply @somipark4990 5 years ago 경찰귀요미춤사라찐 Reply @SophieS-j1f 6 months ago I really like this video, and it is helpful. However, the music was distracting and made me tenser (no pun intended) Reply Physics Videos by Eugene Khutoryansky · 1 reply @Zinebthebest 1 year ago hello, i like your content. Would appreciate it if you tell me which software or app was used to make this video . Thank you! Reply Physics Videos by Eugene Khutoryansky · 1 reply @humanboeing777 8 years ago Question: if you have an orthonormal basis, are the covariant and contra variant components the same? Reply Physics Videos by Eugene Khutoryansky · 1 reply @GreyWind 5 years ago (edited) The increased dot products does not makeup the original vector ?? Reply @ShyamSundar-cv7nr 8 years ago why to multiply the magnitude of the basis vector in the dot product(i.e is vector 2), as the cosine of the vector 1 itself gives the value of the projection..? Reply Physics Videos by Eugene Khutoryansky · 2 replies @somipark4990 5 years ago 실내만있눈 Reply @KevinGomez-od3ee 4 months ago Está cabron Reply @infiniteloops1879 5 years ago One question arises? how can i calculate the contra-variant components of that vector in 3:50. Reply @devendrabisht9713 3 years ago At 0.45 ... Each basis vectors have integral value i.e. 4(yellow), 2(green) and 6(red). Can these individual value be a fraction value too?? Reply Physics Videos by Eugene Khutoryansky · 1 reply @somipark4990 5 years ago 양지영무슨기도할까 Reply @jackieking1522 1 year ago Hi, Ho, Silver. Away!!! Reply @seeker296 8 years ago Okay so now I need to learn what a dot product is =p Reply 4 replies @thevegg3275 7 years ago in keeping to my previous question, I notice when the covariant components double because of doubling the basis vectors, you make the (90 degree notation and the line pointing to the tip of the vector) disappear. is that because it is impossible to keep it at 90 degrees if you change the length of the covariant basis vector? Does changing the length of a basis vector from 1 to any other length (in covariant measurement) change the angle from 90 to other degrees? If so, what is the significance of the 90 degrees at the magic (1) for a basis vector? I assumed that the dot product was the projection of the vector on to the basis vector, but if that is true then changing the length of the basis vector would cause no change to the projection and as such the value of the component in the covariant measurement. 1 Reply 13 replies @sersil1 5 years ago (edited) Why do the projection rules change? 90 degrees - where do they disappear? Reply @mksybr 5 years ago Is a basis vector a vector with only one (non-zero) dimension? Reply @somipark4990 5 years ago 85 Reply @fordtruck105 8 years ago Well done for an intuitive understanding, but could do without the background music which breaks a person's concentration? The William Tell overture was used for the Lone Ranger TV series. Hopefully, uses will be covered in the next video. 1 Reply @rotorblade9508 5 years ago (edited) Supposing we have 2 vectors V and W and x, y axes. Then Vx•Vy should be zero because they are perpendicular to each other?! How does that work? Reply @keness99 7 years ago The background music is to loud and disturbs concentration. Reply @somipark4990 5 years ago 얄지영무슨기도할까 Reply @moimimi9399 2 years ago The music used is annoying and distracting 1 Reply @ismaelmoraes1617 5 years ago Thais is beautiful. Reply @cameronspalding9792 5 years ago Could the cross product be seen as a tensor Reply @LjubisaGavrilovic-mt 5 years ago Covariant, Contravariant = Excellent. Rank = seen elsewhere - jolly good. What is tensor (intuitively?) / explained = 0 - I haven't found a single place which explains 'what is it'. But no worries, that is not exclusive property - I have realized over years that many fail to explain things they think they managed to get explained. (seems it goes with theory of universal relativity) Reply @patinho5589 4 years ago One thing isn’t quite right: You use the word ‘combination’ when you mean ‘permutation’. Reply @somipark4990 5 years ago 락스누가전달 Reply @sunburnt8742 5 years ago the constant rotation in the video gave me motion sickness Reply @riadhasan540 5 years ago How did u evaluate the values of dot products? Reply @mazenelgabalawy3966 6 years ago Okay I still don't get it. Reply @surajawasthi1443 5 years ago How you are doing simulation. Please Reply. Reply Physics Videos by Eugene Khutoryansky · 1 reply @carmatic 7 years ago (edited) can you explain what a dot product is? what does it have to do with 90 degree angles? Reply Physics Videos by Eugene Khutoryansky · 2 replies @nuclearexplosion4881 6 years ago Does anyone know the name of the first piece Reply Physics Videos by Eugene Khutoryansky · 1 reply @jatinbhatia4954 8 years ago how are these videos made? how is this animation done? can anyone help? Reply Physics Videos by Eugene Khutoryansky · 1 reply @DrMcFly28 5 years ago So, a tensor is a bunch of colorful arrows accompanied by classical music. Got it. Reply @sanjaythorat 1 year ago @2:58 If we double the length of basis vectors, the length of basis vector still remains 1 unit, right? So, how will it double the length of dot product? Reply Physics Videos by Eugene Khutoryansky · 1 reply @fereshtehhajiali7935 4 years ago What is the use of these Tensors? What does it mean? I am really confused! Reply @-_Nuke_- 8 years ago So the tensor is the gray arrow? Reply 1 reply @truetruetruly2163 2 years ago I wonder if these videos are scripted or actually handcrafted. Nevertheless, incredible content. Reply Physics Videos by Eugene Khutoryansky · 1 reply @VedanthB9 3 years ago (edited) What exactly does a "combination of basis vectors" in a tensor mean? I can understand that associating a number to a single basis vector gives some sense of "action in a direction," as in the case of a vector. But what does it mean to associate a number to a combination of two basis vectors, for instance? Any real-world examples would be helpful. Reply 2 replies @MarcelloZucchi91 8 years ago Is it correct to say that the covariant and contravariant components are the same for an orthonormal basis? I'm new to tensors and still trying to get a grip. Please correct me if I'm wrong. Reply Physics Videos by Eugene Khutoryansky · 1 reply @prabhavjoshi6147 5 years ago Which software you use to make such good animations?? Reply Physics Videos by Eugene Khutoryansky · 1 reply @ibrahimlakhdar1299 7 years ago contravariant and covariant components are equal in a orthonormal basis,am I wrong? Reply Physics Videos by Eugene Khutoryansky · 1 reply @drover7476 2 years ago Brilliant video but I need a bit of help if anyone is kind enough. Isnt the dot product invariant? When the video says that increasing the basis vectors also increases the dot product (as an example of covariance), isnt the dot product able to be thought of as the projection of V on the respective basis vector? Surely as the angle has to be 90°, the dot product would half if you doubled the basis bector for say x? Thanks in advance Reply Physics Videos by Eugene Khutoryansky · 3 replies @exploreeverything6881 5 years ago Little sleepy though Reply @RTD553 7 years ago All very well. But dot product - well of course everyone knows what that means! Reply Physics Videos by Eugene Khutoryansky · 1 reply @jriosvz 1 year ago third time I'm watching this Reply @devendrabisht9713 3 years ago As described in the start of the vedio..can basis vectors have any orientation????? I mean the three vectors should not be coplaner atleast.. Reply Physics Videos by Eugene Khutoryansky · 2 replies @MrAlexPhilippov 1 year ago 2:51 Субтитры на русском какой-то надмозг переводил, т. к. "dot product" всю жизнь было скалярным произведением, а не "точечным произведением", как в субтитрах. 😅 Reply @saxhorn1508 5 years ago Another comment about the music, I’m afraid. It’s difficult to concentrate on the math if you are familiar with the music. And vice versa. And you know that people who would like to concentrate on one are generally familiar with the other. Respectfully. Reply @somipark4990 5 years ago 내복 Reply @ahmetyusufklc5359 6 years ago But l do not get What the matter of tensor is. Reply @sajil36 8 years ago Hi, I have now words to express my gratitude:-))). If possible, could you please explain, how do you turn such abstract concepts to insights ?(I am sure, if you do so this will change the world). Which software/tools are you using to create these videos?. Can you make a video about Helmholtz equation (https://en.wikipedia.org/wiki/Helmholtz_equation)?. Reply Physics Videos by Eugene Khutoryansky · 1 reply @seandafny 8 years ago who the hell thought of this Reply @pokopokopokopko5724 5 years ago Is this pathway with basic vector? Reply @lsora12 7 years ago Sorry to sound harsh, but I didn't found this very intuitive. Suppose we multiply the co-variant component with the contra-variant components to get this matrix. Sure...you CAN do that, but WHY would you want to that? There is where intuition lies, in my opinion. Reply @arijitkarali 6 years ago What is the name of first music Reply Physics Videos by Eugene Khutoryansky · 1 reply @learningisecstatic9348 7 years ago No background music is required. Awesome video. But background music is annoying and distracting. Science itself is musical and rhythmic. Reply @randy_C44 9 months ago Love the explaination but I hope there are no music. It is very distracting and sometimes I couldn't hear the explainations. Reply Physics Videos by Eugene Khutoryansky · 1 reply @jameshopkins3541 2 years ago THE COMPONENTS ARE NO ARBITRARY LIKE HERE USUALLY THEY ARE PERPENDICULAR TO EACH OTHER Reply Physics Videos by Eugene Khutoryansky · 1 reply @hasemhasan1151 7 years ago Why does the music have to be so dramatic.... Reply @AshishRaiVfx 6 months ago I do not understand when you say that when you double the basis vector, the components also double, in the dot product components. Maybe I should do a refresher on dot product. Reply Physics Videos by Eugene Khutoryansky · 1 reply @dXoverdteqprogress 8 years ago You probably get this question a lot, but what is the software you use to make your videos? I also make physics videos and would love to make them more animated. Thanks. Reply Physics Videos by Eugene Khutoryansky · 1 reply @precogtyrant 7 years ago If you don't mind, may I ask which software do you use for these animations? Reply Physics Videos by Eugene Khutoryansky · 1 reply @textoffice 3 years ago (edited) Cette vidéo m'a permis de comprendre pourquoi les noms de covariant et contravariant. Mais j'ai du ressortir la formule du produit scalaire pour comprendre. Si on a un vecteur de base i et un vecteur A qui fait un angle alpha avec i alors le produit scalaire est (avec les lettres représentant la norme des vecteurs) : A * i * cos(alpha) si on fait un changement de coordonnées I=2i alors le nouveau produit scalaire est A * I * cos(alpha) ou A * 2i * cos(alpha) donc on a doublé le produit scalaire qui est la coordonnée covariante. Mais je ne vois pas comment l'animation montre cela, comment elle intègre la formule du produit scalaire. L'animation fait disparaître les projections orthogonales des vecteurs au moment où on double la longueur des vecteurs de base avouant ainsi que la représentation ne représente rien. On ne peut comprendre la vidéo que si l'on a intégré la formule du produit scalaire. Donc la vidéo ne donne pas une représentation intuitive car on doit faire référence au cerveau gauche pour aller chercher la formule du produit scalaire. Reply 1 reply @detouredbriefly9426 8 years ago button me up will ya? Reply @akshays949 1 year ago Background music was not necessary Reply @thevegg3275 7 years ago I agree with Jesus. Also, if the dot product of a vector is tantamount to the projection of the vector on the basis, why would increasing or decreasing the basis increase or decrease the number. The projection is the same no matter the length of the basis. Thanks for your great animations. Reply Physics Videos by Eugene Khutoryansky · 1 reply @olgagerman4878 3 years ago So basically these videos make schools useless. This is what I will show my future children for sure. Absolute gem. And it's for free, damn... Reply Physics Videos by Eugene Khutoryansky · 2 replies @somipark4990 5 years ago 앨범안다문화아닌 Reply @benlee93 4 years ago What program did you used for this visuliazed explanation?! Reply Physics Videos by Eugene Khutoryansky · 1 reply @jamest.5001 8 years ago I insert promotional comment here? I hope every one sub's this channel... Reply @danwoodall8629 7 years ago The music is distracting Reply @-channel713-2 7 years ago Умоляю, сделайте перевод на Русский Translate in Russian, pleeeease Reply @dkkempion8744 8 years ago Tensors, probabilities and the the cosmological constant are ALL fuzzy math and non sequiturs. They declare "we don't know" first, then "let's try something basic we can use as a stop-gap until we know more." Challenge me. Please. I'm no physicist but I have the ace of spades. Reply @semgor5698 6 years ago What is a music on 9:00? Reply Physics Videos by Eugene Khutoryansky · 1 reply @sunilperera4837 5 years ago Pbbperera Reply @Emboaba 5 years ago What is the software used for these video Many thanks Marcus Reply Physics Videos by Eugene Khutoryansky · 2 replies @jamesjenkins9480 8 years ago What do you use for visualization? Reply Physics Videos by Eugene Khutoryansky · 1 reply @shaunmike 8 years ago (edited) How do you make these videos? What program? Also, how do you arrive at such incisive thoughts? Are you a genius? Do you read quite a bit? I'd like to know your methods. Is it honestly even possible for someone just above average? Thankx Reply Physics Videos by Eugene Khutoryansky · 1 reply @nyetliu 8 years ago I do not understand non-orthogonal/orthonormal basis vectors. Reply 2 replies @somipark4990 5 years ago 1000원앞머리5천원돼지고기 Reply @thevegg3275 2 years ago Ok, after months of thinking on this, I have an explanation of covariant vs contravariant that no one has ever uttered, as far as I know. Here goes. Hold my beer! ——— You combine contravariant (components times their regular basis vectors) tip to tail to reach the tip of the vector you're defining. But with covariant, you combine (covariant components times their dual basis vectors) tip to tail to get to the tip of the vector you're definging. Why does no one explain it like this? But my question is how is covarant components of dual basis vectors relate to the dot product? Please correct me if I'm wrong on the following... DOT PRODUCT: A (vector) dot B (vector) = a scalar quantity CONTRAVARIANT: described by the combination of contravariant (components times regular basis vectors) added tip to tail of A (vector) dot B (vector). COVARIANT: described by the combination of covariant (components times dual basis vectors) added tip to tail of A prime (vector) dot B prime (vector). QUESTION: If we dot product A prime (vector) with B prime (vector), does that scalar quantity equal A lower 1 prime times e upper 1 prime PLUS A lower 2 prime times e upper 2 prime? If so, arent we then saying that a scalr is equal to a vector??? Reply @inf5329 7 months ago the music is so loud and annoying Reply @eugenepohjola258 6 years ago Howdy. What is the big deal with tensors ? A rank 2 tensor simly represents two physical properties in the same point of space. I.e. one vector may describe the electric field''s strength and direction and the other the magnetic field's strength and direction. So what ? Why just not let there be two vectors ? I suspect the big idea is that it is somehow easier, or more powerful, to process tensor math than separate vector math. Reply 1 reply @ckpsolutions7300 7 years ago (edited) ma'am may i ask which software do you use to make videos Reply Physics Videos by Eugene Khutoryansky · 1 reply @graysonparker1593 2 years ago …as someone who does not know math very well…all I’m seeing is taking arbitrary representations of different vectors and finding different ways to mash them together and then giving it a name…what is the point? Reply @masterburgn 7 years ago great video but no music needed... its horrible. Reply @david203 6 years ago The back and forth rotation of the whole think made me dizzy. Really. Reply @theokenric 2 years ago Let's see Paul Allen's explanation of Tensors 2 Reply @somipark4990 5 years ago 엄마성우 Reply @anandnataraj6599 7 years ago How do you make these animations? Reply Physics Videos by Eugene Khutoryansky · 1 reply @MichaelElKadi 4 years ago Hello, could I ask you what software you use to create these visualizations? Thank you :) Reply Physics Videos by Eugene Khutoryansky · 2 replies @robertturpie1463 5 years ago Speed this up by a factor of 2. It’s too slow. Reply @somipark4990 5 years ago 임가령 삼성며느리 둘째 Reply @ChevroletCamaro2970 6 years ago Ты есть в ВК? Reply @furzkram 7 years ago Audio way too low Reply @CamEron-nj5qy 3 years ago Music? Reply Physics Videos by Eugene Khutoryansky · 1 reply @psient 8 years ago Sir, I do not see the ethics of no 'this video' on your patreon place. Also the narrator is an important instance of attention. Reply @zes7215 7 years ago (edited) no such thing as way or usual or not, say anyx Reply @111ark 5 years ago Very dramatic, indeed. Reply @somipark4990 5 years ago 꼭 미국가서 결혼하려눈 Reply @robertcollins1776 7 years ago The video seemed to do a good job, but the background music was so distracting that I gave up about halfway through. (I liked the music, and I liked the video, but I could not understand the narrative because of the music.) Remove the music and you will have a much better video. Reply @JsCEbsVe 1 year ago What kind of software is used to make this kind of video? Reply Physics Videos by Eugene Khutoryansky · 1 reply @zeynab3304 3 years ago nice view but terrible background music Reply @Copperbuns 3 years ago What's a dot product ? What's a rank ? Reply Physics Videos by Eugene Khutoryansky · 2 replies @BaronOfTeive 1 year ago Music is not necessary Reply @andrewking8616 6 months ago Let's agree to destroy all quantitatively subjective vector space translation through subscripting conventions Reply 1 reply @somipark4990 5 years ago 좁은차수위집가정부 Reply @MrRoboticWarfare 8 years ago So essentially, a tensor of this type is simply a collection of information? It's not entirely intuitive to me how one would apply this kind of tensor to something else. Reply Physics Videos by Eugene Khutoryansky · 2 replies @gianki83 5 years ago You videos are cool, but the music is distracting to follow the explanation. Reply @Walter-uy4or 4 years ago Nice take, but the music was irritating and distracting. Reply @nehalkalita1 3 years ago Your content is good and simple but the background music in almost all of your videos are annoying. 1 Reply 4 replies @ankurc 6 years ago Music by? Reply Physics Videos by Eugene Khutoryansky · 2 replies @somipark4990 5 years ago 남자속귀신여자겉혀 Reply @EV4UTube 4 years ago I Love the video, but all the swaying movement make me sea-sick & nauseous. Reply @JoeRussell-oj7xm 2 years ago The background music you have chosen is too rich and emotional, it distracts from the presentation. Reply @dagoninfinite 7 years ago Too quiet Reply @MTB_Nephi 7 years ago PLease stop this background music :) Reply @lawliet2263 3 years ago Who is the woman ♀️ behind these videos? Reply Physics Videos by Eugene Khutoryansky · 1 reply @somipark4990 5 years ago 성격파탄자교사근무수술남자 Reply @christhomasson4972 5 years ago Are you making these in PovRay? Reply Physics Videos by Eugene Khutoryansky · 2 replies 5 years ago What's up with the depressing music? Reply 1 reply @MilesBellas 7 years ago Classical music not needed and distracts Reply @iosonoscarpia 5 months ago Why did you add music. It's very distracting - and disrespectful toward music. Reply @somipark4990 5 years ago 비추이가박정훈 Reply @martinhirsch94 6 years ago Whatever Reply @skinslayer808 7 years ago The graphics are a brilliant way of explaining multi-dimensional components, but a generic comment: Dear Educators, please don't put music of any kind on the presentations. It's very distracting (annoying, even). Inversely, imagine going to a concert and having a voice-over throughout! Reply @somipark4990 5 years ago 유재석박정훈결혼회관망함 Reply @knoxvillelee8642 2 years ago BGM is annoying... Reply @CarolHaynesJ 5 years ago (edited) Your explanation is good but the background music is incredibly distracting. Why is it necessary? Reply @joudjoud1947 7 months ago Why this ugly music ! It spoil everything ... Reply @МаксДамагехаз 4 years ago Ещё б музыку убрать. Отвлекает зараза. Reply @xelth 7 years ago Дикторше явно пох на то о чем она рассказывает... Reply @dionisiocarmoneto 3 years ago Господа или дамы, Я не понимал, почему фигура должна все время танцевать. Это мешает рассуждению и визуализации, которые делаются. Я считаю, что можно было бы сделать новую версию, не нуждаясь в движениях, которые появляются в векторах. Извини, я просто хотел быть честным. Я думаю, что это стоило огромных усилий, но результат был чрезвычайно разочаровывающим. Спасибо большое Reply @nagys36snn 6 years ago Sleep Reply @thevegg3275 2 years ago (edited) I don’t understand covariant components. I see no method of obtaining the vector length by combination of the components. And no method is explained like it is with the contravariant. From what I see right now, it doesn’t seem that covariant components are really components at all because components add together to create something and these numbers, do not combine any real sense to point to the tip of a vector Reply 1 reply @sambringit7859 7 months ago Annoying music Reply @tiborfutotablet 2 years ago Why the music? It damages the quality of the video. There is no problem with no music at all. Reply Physics Videos by Eugene Khutoryansky · 2 replies @dr.z101 2 years ago (edited) Great video as usual, I hope you clear up a simple problem with me, at the beginning of the video. I notice that the projection component of the white vector in the direction of the yellow base vector, after changing the base vectors, must be -4, not 4. Is my point valid? Or , when are project the vector, the projection must be parallel to the red base, and therefore it fell in the positive part 1 Reply Physics Videos by Eugene Khutoryansky · 3 replies @foreverseethe 7 years ago I don't find this intuitive in the least. Misleading title. The term intuitive should be reserved only for concepts that laymen can generalize from everyday experience. Reply @tlalicetears649 5 years ago I felt dizzy after 3 minutes, stop rotating pls Reply @dhavaldeshmukh3653 6 years ago Are you a boy or a girl ? Reply @JRondeauYUL 5 years ago Pourquoi un titre en français????? 🤪🤪🤪🤪 Reply Physics Videos by Eugene Khutoryansky · 1 reply @Julian-tf8nj 1 year ago I was soooooo distracted by the music 😵‍💫 Powerful music like that COMMANDS attention : a constant fight against it... Your video would be 10^500 times better without music, or at least more mellow and less-loud music Reply Physics Videos by Eugene Khutoryansky · 1 reply @seanthomas5303 5 years ago At 1:07 you're talking about dot-products without any intuition about what it means to do a dot product, which is simply a way of extracting the similarity of a vector to another vector. If you're going to claim something as 'intuitive' then it shouldn't rely on unintuitive abstract concepts. Reply Physics Videos by Eugene Khutoryansky · 1 reply @soumyagupta7637 4 years ago ur music is not good Reply @bi4229 5 years ago Please turn down the music Reply @FrazerKirkman 7 years ago After 2 minutes, you no longer explain anything, you are just making definitions. I wish you had explained why you would multiply those different basis vectors together. Reply @SayantanM7 6 years ago annoying sound Reply @aminassadi5104 5 years ago The music is so irrelevant to subject Reply 1 reply @jayarava 7 years ago By the end I am slightly sea sick from the swinging motion of the figures. It adds nothing by distraction. And the William Tell Overture is also just distracting. I'm trying to concentrate, but you keep interrupting me. Any animation effects or music should contribute something to the learning process - not add random bits of non-essential information. This is poor pedagogy. Reply @touristguy87 10 months ago How can tensors be explained "intuitively"? Good grief! Of all the nonsensical statements. Reply @bobcarver5231 5 years ago The music is distracting and for me ruins the otherwise beautiful presentation. Really frustrating for musical people. Reply @Mathin3D 3 years ago FAIL Reply @nathanielscreativecollecti6392 7 years ago This is making me sick... Reply @andrisszalai1261 6 years ago This music doesn't match the video. Like at a hearse. 2 Reply @matej.vondracek 3 years ago Bruh whats up with that music 2 Reply @madanjeetsandhu7580 4 years ago This starling bank advet is one of the most intrudive snd irritating ads around get rid of it please Reply Physics Videos by Eugene Khutoryansky · 1 reply @Old_Doc25 1 year ago Would love a version without the music. Very annoying. Reply Physics Videos by Eugene Khutoryansky · 2 replies @ehud8an 3 years ago Hi why not take/turn off the music? it disturbs me a lot. 2 Reply @MrDeep414 7 years ago I dislike this video, due to I can not concentrate on text. Remove music please! Reply @artyquantum7283 5 years ago I love your videos. But this video is just swinging too much my head started hurting trying to focus on vectors shown. Kindly dont rotate anything this much again and again :( Reply 1 reply @frankkolmann4801 2 years ago (edited) Intuitive? Muah! Every time I started to assimilate a comcept raised that idiotic music cut in and completely derailed my thought. I know dot product and basis vector but if you only have a vague idea of these concepts then your explanation is meaningless. Even so Iost what you point was. As for an intuitive explanation of tensors! You make me laugh. Ha Ha Ha .Ha Ha HA HA HA not even close Reply @cooldude6975 2 years ago Please stop with the music !! It’s very very irritating !!! 2 Reply @1_1AZH 3 years ago Что-то я больше не понял, чем понял Reply @klick2destruct 7 years ago Nothing against William Tell but this tutorial combined with the monotonous voice feels like someone's dying. Keep it light on the music, would you? Reply @ВсеволодПарфёнов-ф2ъ 9 months ago After this explanation I understand less then before. 1 Reply @alangoodfaith2262 9 months ago I had reached 4'50. Reply @markusgairing9171 2 months ago Unfortunately you do not say that the Vector can be described first by the covariant Basis and the contravariant components and secondly bye the contravariant basis and the covariant components. What you call covariant description of the vector is misleading. So vector v can be written as v= v1*E1+v2*E2 = V1*e1+V2*e2. The Genus ideal of this concept is exsctly this that you always have the Kombination of contravariant and covariant and vice versa . Reply @debasishraychawdhuri 8 years ago Really good quality video and explanation, horrible background music. Reply @yeknafaskesh1257 8 years ago The music is too loud and very distracting. Reply @neutronenstern. 11 months ago a lot of visualisation, but no explanation Reply @gorech2009 2 years ago Это бред сумасшедшего Reply @wiseguy7224 4 years ago (edited) Excellent explanation. You could speed up a bit, though. But the background music ist extremely annoying and distracting. Thumbs down. Reply @Confirmed-Humanist 1 year ago The music is cool. It needs to be louder. The content is otherwise garbage. Reply @texanplayer7651 5 years ago I will give this video a dislike because when the william tell ouverture popped up I just had to go listen to it and forget everything I just learned from this video. No I'm just joking, excellent work! Reply Top is selected, so you'll see featured comments