What's a Tensor?

What's a Tensor? Dan Fleisch 56.7K subscribers Subscribe 141K Share Ask Save 4,139,821 views Nov 20, 2011 Dan Fleisch briefly explains some vector and tensor concepts from A Student's Guide to Vectors and Tensors Chapters View all Transcript Follow along using the transcript. Show transcript Dan Fleisch 56.7K subscribers Videos About 5,689 Comments rongmaw lin Add a comment... @wirechair 6 months ago who's rewatching in 2025 again before going to bed?? 931 Reply 46 replies @shaulpagis-sharon4484 3 years ago A tensor is a tensor that behaves like a tensor - my actual Physics professor 265 Reply 9 replies @E8oL4 2 years ago when your wife and kids are out and you have a free sunday 100 Reply 1 reply @dalnayak 2 years ago video: 360p explanation: 4k 12 Reply @antoinefdu 5 years ago "Thanks very much for your time" Dude. Thank us!? Thank YOU for your time! 2.5K Reply 11 replies @gilzam9183 7 years ago I love how he says at the end thank you very much for your time, when in reality he went out of his way to try and express tensor in laymen terms for us. 3.9K Reply 17 replies @postalci95 5 years ago Brilliant and simple explanation. It reminds me the quote: "If you can't explain it simply, you don't understand it well enough." 1.1K Reply 18 replies @falconbmstutorials6496 2 years ago You deserve a show in TV with an entire crew of assistance and a audience! Thank you sir!!! 5 Reply @NotDogda 3 years ago As a theoretical physicist it's one of the best simple explanations for a tensor I've ever seen. Thank YOU for your time. :-) 871 Reply 15 replies @Shay_GPT 3 years ago I am a Space Operations Engineer. I have been using vectors for most of my professional life. And I have to say that this is by far the best and most dedicated explanations I have ever seen in my life, either online or offline. I bow to you sir. 631 Reply 1 reply @toddpnewton 5 years ago No Mr. Fleisch, thank you for YOUR time. Without exaggeration, this is one of the best educational videos I have seen on any subject: evenly paced, concise, clear and direct. 2.3K Reply 9 replies @samhudson1169 2 years ago Looks like you haven't posted for a while, so I hope you're still doing OK. Just letting you know that people are STILL getting huge value out of this, 11 years after you made it. Thank you so much 222 Reply 2 replies @vigneshr2438 5 years ago Mildly teared up when he says "Thank you very much for your time" 353 Reply 3 replies @RalphDratman 10 years ago This video is a good example of the educational riches accumulating on youtube. In fact I hate to use the word educational, because it might evoke stiff, uncommunicative academia. But the learning culture on youtube is just the opposite of that. Here we find people passionate to pass their understanding along, filling in a thousand little corners of knowledge. I think we are in the early beginnings of a historical period in which the internet rewrites most of the rules and experiences of human society. I find it thrilling to be living in such an amazing moment. 8.9K Reply 165 replies @yokcos 9 years ago Nononono Dan, thanks for your time. 2.3K Reply 13 replies @MrBerryK 11 months ago 6:23 Cute the ways he made the model vector 5 units long so a 3-4-5 triangle would work! 7 Reply 1 reply @MartinLaBelleIV 11 years ago You gotta love a guy that teaches you something and then thanks you for your time. 6 Reply @richardrichards9180 4 years ago This guy is proof that if you want to teach, it's not enough for YOU to know your stuff-you have to have the ability to communicate it to those who DON'T know. 814 Reply 7 replies @uva1312 6 years ago Damn the twelve minutes flew by in an instant. Incredible explanation. 322 Reply 1 reply @planlosuns 1 month ago After 25 years , i finally understand the actual concept now! Thank You! Reply @19ghost73 6 years ago 624 scalars disliked this video! ;) 1.4K Reply 19 replies @julesm3334 3 years ago Without a computer graphic or computer for that matter anywhere, this was probably the clearest illumination of vectors and tensors I've ever watched. Outstanding. Genius in it's simplicity. 30 Reply @iron_blood7 5 years ago At the end, he said "Thank you very much for your time" but actually we have to thank You for your time! 57 Reply @rcRaghu 3 weeks ago Almost in tears .. Wish we all get more physics teachers like you 🙏 Reply @nicorobin7666 6 years ago You can feel him putting a good heart into his explanation, ❤ 102 Reply 3 replies @flimspringfield3975 6 years ago next up: how to deduct your kid's toys on your taxes 598 Reply 3 replies @whaddoiknow6519 1 year ago Magnificent! The final comments beginning at 11:20 are probably the best part of the video. I suspect Dr. Fleisch would be able to tell us more about this aspect in an equally brilliant way, but that would require another 15 minutes. 16 Reply @awesome-kartikey 10 months ago 13 years ago and this is still the best video on tensor. Reply @brendanlarson3432 5 years ago This man is so wholesome. We must protect him at all costs. 1.4K Reply 26 replies @ZoeyTangCRE 5 years ago (edited) I’m in love. YouTube actually had quality content that was worth subscribing for, 10 years ago 23 Reply @juanfranciscojesushernande3396 9 years ago 👌👏👏👏👏👏👏👏👏👏👏👏👏👏 this is a great methodology, it is a mix of old school and new media, but what really makes this awesome is the professor's attitude and charisma. Keep on doing an excellent job. 👍 423 Reply 3 replies @PrimataFalante 6 years ago Such a masterpiece in science communication! Saw it the first time years ago, when I first started to learn Tensor Calculus, but I still learn something every time I watch it again. 719 Reply 4 replies @sasoptimis 6 years ago I have many many textbooks, and I have never seen anyone explain vectors and tensors as well as him. 631 Reply 25 replies @atyantkumarhota 5 years ago Einstein was right. I couldn't feel the 12 mins, while the lectures of my university feel like decade. 104 Reply 2 replies @Alphonso7777777 2 years ago Tensors entered the explanation before it was even explained what a tensor is. Initially thought I missed something and listened to it twice. 2 Reply @brandonscheiber7866 3 years ago This video is a blessing, it shows the true potential of youtube for education 67 Reply @mrgaudy1954 9 years ago Educators like this are worth their weight in gold, particularly when dealing with the often abstract and seemingly intangible concepts of mathematics. Great demonstration. 10 Reply @borg972 8 years ago 0:00-11:20 I feel like he's speaking to me as if I was 5 years old. 11:20-12:00 I can't understand what the hell is he talking about.. 780 Reply 39 replies @maoam-im7lc 1 month ago This video is still a banger in 2025, I hope everyone in the comment section and you are doing fine! Thanks Dan! Very helpful! 2 Reply @maidy199 8 years ago Meanwhile, a child is wondering where all his toys went 452 Reply 13 replies @OmNamaShivay79 4 years ago Extremely well explained...I wish we had more teachers like him. 226 Reply @Aieieo 1 year ago You know it’s gunna be good when the audio hits you with the fuzz 2 Reply @abdullahsulaiman8055 2 months ago The best video that explains tensors on YouTube! Reply @MazdakNation 8 years ago This is excellent. Only wished had found it 30 years ago. 130 Reply 3 replies @tushargumber5655 3 years ago Today I studied tensors for the first time in my msc maths class and didn't understand anything but when I searched about it on yt this masterpiece video appeared and now I'd say I know what is tensors. Thanks a lot sir for this practical demonstration of tensors. We need teachers like you in our indian education system. 109 Reply 1 reply @RexGalilae 10 years ago 12:15 It's me who should say "Thanks very much for your time and effort!!" ^_^ 75 Reply 3 replies @THELONIOUSMONstertrucK 2 months ago He's a physics teacher with ninja skills. We need more of him Reply @tomahzo 2 years ago During my 5 years at university going through my undergrad studies I might have had one teacher like this. Going through higher level education is like an endurance test. If you succeed it's despite the teachers rather than thanks to them. If every teacher was like this guy (or if the teachers at least tried) then it would have been a joy through and through. Sad state of affairs, really, but it's very nice to see someone teach who knows how to do it properly :). 131 Reply 11 replies @AIQuotient 5 years ago This is probably the best explanation of a 'Tensor' out there! Great illustration of the 'Feynman Technique'. Thanks, Dan for all the effort! 42 Reply @colinjava8447 9 years ago I feel tenser after watching that, good video! 116 Reply 3 replies @josephbolton8092 2 months ago When I saw the props I already knew this was going to be pure gold. Reply @shanebenjamin7519 12 years ago This is the most amazingly clear and simple explanation of Tensors that I have ever seen. Well done sir. 5 Reply @prajwaldeepkamble6617 5 years ago Can anyone take a minute to appreciate how beautifull he made us visualise vectors without animations like 3b1b You really can't tell which is better both are great teacher. Sir Feynman must be smiling from above. 328 Reply 3 replies @AShiga 5 years ago (edited) 15 years after college and finally understood it right off a random yt suggestion. I came here with no goal and learned something really complex! Thank YOU Mr. Fleisch! 9 Reply 1 reply @Łukasz-h4i 7 months ago You are not only a great teacher but also a director. Reply @rolfvanderbijl 3 years ago I think only someone who loves his field of interest and is actually compasionate and understanding about it, can explain so calmly and clearly. In my experience, that's the best way to learn. Thank you for this explanation Mr. Fleish! 27 Reply @ahmedovsky7166 2 years ago I am a master's student in physics, and this is the first time I understand vectors and tensor with such clarity Thank you for this effort and your time I opened your channel and saw that the last video was uploaded 3 years ago I hope you are well. 17 Reply @ukno918 11 years ago Revealing, especially after linear algebra. This stuff is so powerful. 19 Reply @CC--qn4gf 5 months ago This has to be the best explanation of tensors I have ever seen. Reply @tearsintherain6311 3 years ago (edited) This is maybe the best video or teacher interaction I have had in my life , I can’t believe it, it’s so well crafted and I understood it perfectly thanks to his way of explaining and showing it in the real world. I envy the students of this man. 41 Reply 1 reply @BTC_DNA 9 years ago You just did a better job of explaining tensors in a 12 minute video than 4 years of Mechanical Engineering. Where were you twenty years ago?! lol Great job, Dan. Thank you. :-) 5 Reply @acho8387 9 years ago So Michael from Vsauce has time traveled to the future? 490 Reply 12 replies @danieljrossofficialmusic 1 year ago The blocks and pins helped morph the math into understanding 1 Reply @qusapiens 6 years ago I haven't seen such a beautiful explanation since a i learned what's an integral. What a work !!! 59 Reply @Ysehporp 2 years ago This is incredible. I just finished a course on data visualization from one of the most accomplished professors in data visualization. Some of his works have many thousands of citations. Despite that, his explanation of tensors was nearly incoherent so I went through the whole class without understanding them. Yet your 12 minute video did what his whole course couldn't. Thank you so much! 9 Reply @dilipsaraftopcoach 10 years ago Thank you very much for a lucid explanation of tensors and for making it very graphic and so easy to grasp. You have a gift of making your readers understand! 5 Reply @DheerajNarlajarla 5 months ago Sir, I'd be eternally grateful for this explanation Reply @donmiller6485 6 years ago I subscribed when he used the light shadow to demonstrate the x axis, even though I couldn't see the shadow, what a great idea. 28 Reply @jasonm3835 11 years ago You sir, are a fabulous teacher. 4 Reply @saf271828 11 years ago This is the first time I've had any understanding of tensors. I'm still not fully appreciative of the implications, but at least I finally can see their value in descriptions of physical phenomena. 7 Reply @xennial7408 2 months ago Someone I could listen to all day. Reply @markmiguel7508 2 years ago Sir, you are exactly what's missing from education. It is so seldom that one gets such excellent explanations. I really value how you take the time to build up on these concepts and leave away the maths for a moment to explain exactly what a tensor is. Far too often we have lecturers diving in headlong into the mathematics of it all without explaining what it all actually means. Thank you for your willingness to share your knowledge with the world. To you, sir, I take off my hat! 7 Reply @zejalt8608 8 years ago What a great teacher. The explanations are just so clear 25 Reply 2 replies @sietsebuijsman8523 11 years ago Thanks a lot! This video helped me understand Tensors better, which is quite important for my upcoming Electrodynamics exam. Keep up the good work. 4 Reply @Fejimush 2 years ago Old video but best simplified description of tensors by far. Reply @stevensenger 2 years ago Wow... tenured math prof here. I've always struggled with tensor explanations as either too abstract or too concrete. You've struck a wonderful balance here! Thank you for your hard work! 10 Reply 2 replies @OldShadeOfBlue 11 months ago Start losing me around 8:20 8 Reply @abc6450 12 years ago WOW, that was an awesome explanation! 5 Reply @james-t-lucas 2 years ago If only all maths lecturers taught in such a clear and concise manner Reply @crogersdev 6 years ago Heh. I'm literally looking at the building blocks of tensors. 124 Reply 2 replies @TheForbinExperiment 1 year ago Outstanding. There are teachers, Teachers and TEACHERS; and TEACHERS like this are all too rare. It’s a special treat to take a masterclass from someone so thoroughly across the material, that they have the ability to simplify the complex. Thank you. 246 Reply 1 reply @randyrandom5702 6 years ago You had me at "Small arrows" It is a Nerf Whistler Dart otherwise known as the Sonic Micro Dart circa 2003. I liked and enjoy the video :D 35 Reply @dencybk 2 months ago (edited) Wow. These are kind of explanations which every maths/physics students needs to understand the subject better!! Reply @dennisleas8996 3 years ago Dan, you are a gem! Thank you so much for putting this together! If we get you a bigger table, can you explain quantum mechanics? Please? 19 Reply 1 reply @oliverbecerragonzalez7751 8 years ago Professor Fleisch. First of all I want to congratulate you for such a simple yet wonderful to explain what a tensor is. I wish I had a professor like you during my bachelor, because people like you, that devote to make complex concepts easy to understand to people are true Masters. I am looking forward in the future if you could upload more videos like this. 25 Reply @SciHeartJourney 10 years ago Professor Fleisch is also the author of this excellent book that I'm reading: "A Student's Guide to Maxwell's Equations". Excellent book! 12 Reply 1 reply @hpatelecom1 2 years ago I bow down to you sir. I wish someone explained math like this to me. Reply @frankbholle 6 years ago Thanks Professor Fleisch for your work. I really appreciated your book "A Student's Guide to Vectors and Tensors". 10 Reply @noahhysi8622 5 years ago Thank you Dan Fleisch! I'm on my way with learning Linear Algebra but I've never come across an intuitive explanation of a tensor until now! 10 Reply @R4CrEntertainment 6 years ago I think this is one of the best videos I have ever watched in my whole life. 5 Reply @thanosathanasopoulos7529 8 months ago Truly love the way he talks. Everything is explained obscurely well. Reply @benjamincordes207 9 years ago Dear Dan This video really helped me understand tensors for my course i solid state physics. I liked that you used physical explanations because they are very intuitive and easy to remember. I would love to see you make a video about eigenvalues/eigenvectors in a similar style. I know this has been mentioned before in the comments and it's another very important concept in physics and mathematics that a lot of students have problems with. PS. Please don't take rude comments seriously and I hope they don't discourage you from making more videos that would be such a shame. With half a million views you are going to get comments from some sad immature people. I would bet that 99.9 % of people watching this video found it helpful and are very grateful. (as reflected in the many views and likes) 13 Reply @Alley00Cat 9 years ago The power of representing data as tensors is that you can do matrix algebra on them. If you program, you'll appreciate that this decreases computation time by orders of magnitude when compared with loops. 40 Reply 1 reply @iycgtptyarvg 7 years ago Very informative! When you said, "scalars are tensors of rank 0" it clicked for me. Thanks! 46 Reply 3 replies @craigfowler7098 1 year ago I did physics degree 30 years ago and was always confused what tensors were. Knew they were vector based but this has clarified a lot. Thanks man. 2 Reply @kleemc 9 years ago Best explanation of tensor i've ever heard 6 Reply @protocolfree 1 year ago one of what ? one of whatever units you're using in your system " the hardest concept that i have to explain to someone " 3 Reply @SreenivasanRS 3 years ago An amazing explanation, I never knew what Tensors were about until now and now everything just fits in the puzzle. Thank you! 4 Reply @GG-fd31 1 year ago Thank you for YOUR time and effort, Dr. Fleisch. Reply @viktors783 6 years ago This reminds me of my university math classes, the simplest technical things were explained in the greatest and often tedious detail but the conceptual information on how to think about mathematical objects, map them to reality, compose and operate them to solve arbitrary problems was given in a single-breath tough to chew definition at the end, if at all. I always appreciate the effort, don't get me wrong, but whenever I come across math it feels like knowing the alphabet without the ability to read anything. 12 Reply 2 replies @googleuser1818 10 years ago jemand hier aus RWTH ? :D 28 Reply 5 replies @jhenafiberafin 3 years ago I've just been introduced to tensors in my university mechanics class and didn't understand anything and have been struggling to find a good explanation of what it is and now I finally did, thank you very much!!! 4 Reply @dkhundley 2 years ago If I travelled back in time to show great mathematicians like Pythagoras or Newton this video, it would blow their mind that we live in this golden age where anybody has access to understand a complex topic in as simple terms as possible. This video was a gift! Thank you. 1 Reply @robk5969 6 years ago takes 20 seconds to say "im going to take 12 minutes to teach this" then takes precisely 12 minutes to do exactly that and not a single whiteboard marker or crappy animation in sight 334 Reply 7 replies @pepecohetes492 10 years ago Very clear explanation, thank you! 4 Reply @superstringcheese 9 years ago Thanks for the effort you put into this. Very well explained. 66 Reply @GooberNumber9 2 years ago I've been trying to understand tensors for about 25 years. Now I FINALLY understand them! Reply @aghakhanieng 6 years ago One of the best intuitive descriptions of vectors and tensors I saw in my life!!! As an Engineer I never heard a better explanation. 29 Reply 6 replies @ShrimplyPibblesJr 3 years ago (edited) You sir, have an amazing gift at illustrating in a way where anyone can understand the maths of basic physics. I was just trying to review what a tensor was because I couldn’t quite remember. I had an amazing college physics teacher, I will say.😊 6 Reply @eltonago2200 3 years ago As a student researching astrophysics whose struggling with tensors, this was EXACTLY what i needed. thank you for the time and effort put into this video 18 Reply 1 reply @jonathannetherton6727 2 years ago I spent years failing math classes and barely grasping what I thought were obscure, arcane, and occult concepts, and I learned more about higher-level math in ten minutes than I ever got through in college in three years. Reply @mjw120046 6 years ago Excellent, very well done. I took a few physics classes in college (25 years ago, m'kay) and bumped into tensors a few times then, but I couldn't have told you what they were or why they were important until just now. 6 Reply @himanshubhusanrath8036 4 years ago Sir, you are awesome. I can never think of such concepts to be explained in such a detailed and clean way! Thank you so much for your effort. Simply what a beautiful teaching style. 5 Reply @johnbrandolini2915 8 years ago Thank you very much for the excellent explanation of tensors. I had a passing understanding of them as being a multi-dimensional way of expressing physical phenomena but seeing it explained your way made it clearer. The cube prop reminded me of an array of arrays something I used in programming to build an inventory database many moons ago. I'm a retired EE amateur radio operator who spends his time tinkering at the bench with micro-controllers and RF projects and really likes to keep my mind sharp by pursuing these topics. I wish that when I was in college the professors I had used visual aids such as yours to explain their topics. Ignore the naysayers. ^5 6 Reply @Propane_Acccessories 2 months ago The best teachers and professors I have ever had all wore vests. It can't be a coincidence. Reply @cetx 2 years ago (edited) I missed the part where "tensor" was defined. I understand that vectors can be represented by an array, but at https://youtu.be/f5liqUk0ZTw?list=TLPQMTcwMjIwMjO3KnY7dUcDxw&t=491 Dan suddenly equates the array representation to a "tensor of rank one". What's a tensor, and what's a rank? Is "tensor" the name of that array? And if so, what's the difference between the vector itself and the tensor? 3 Reply @jarod997 4 years ago You've just made all the visual math, physics & engineering learners extremely happy! 7 Reply @kinngrimm 3 years ago Thanks for the refresher. Even in a different language than my mother tongue your lesson was for me simple to understand, which speaks to your teaching ability. I make sure to come back for other concepts i may have once learned in school =) 4 Reply @RiseAnewLion 2 years ago Always wished to have a teacher like you, I learned fast and easily, thank you 2 Reply @oldyoutubevideos7430 7 years ago Best explaination of a vector...I ever heard 10 Reply @jzero4813 9 years ago A pointed stick?! Getting all high and mighty, eh? 22 Reply 1 reply @sarthakgirdhar2833 6 years ago Why is his voice so amazing to listen to? 😂 12 Reply @disqusrubbish5467 4 months ago 13 years later I hope this finds you well. This explanation is excellent - thank you. 2 Reply @SyamVenugopalan 5 months ago Amazing. I studied tensors 12 years ago during my masters and then never used them. So refreshing to see a simplified explanation of it! Reply @raymangoel5372 4 years ago I am very very grateful to you sir !! Never ever expected such a beautiful explanation to rather seemingly concrete mathematical idea . You are an inspiration to the generation of teachers!! ☺️🙏🏻 6 Reply @navisingh9394 2 years ago 11 years later this is still one of the best educational videos explaining tensors, I’m trying to understand how tensors are used in diffusion tensor imaging and this is the only video that’s made it make more sense, thank you 5 Reply @PHHE1 4 years ago I love how he delivers a very basics oriented explanation trying to really explain it well and then as motivation in the end drops two sentences about reference frame transformation that no one with only basic insight into the topic will understand even remotely XD 22 Reply 1 reply @vivaanrao2022 6 months ago Very nice and interactive explanations of Tensors... 1 Reply @lefterisloghis313 6 years ago Thank YOU very much for your time! Neat, clean and simple explanation of the subject. 5 Reply @youtubehandlesareridiculous 10 years ago This was amazingly clear and concise. Nothing that I've ever seen, explains this topic quite as simply and elegantly. Thank you! 7 Reply @pacrii 8 years ago Excellent. An explanation deserving .5 million views. 4 Reply 2 replies @Forkid233 2 years ago best video i wish i had a teacher like you 1 Reply @CoronelOso 10 years ago thank you, thank you, thank you, THANK YOU!!! I love you! <3 4 Reply @dan0themano575 7 years ago This guy is amazing.... honestly, great explanation. 6 Reply @tylerbakeman 2 years ago Tensors are commonly used in math. Examples of tensors include Matrices (vectors of vectors of scalars) and are tensors of “rank-2” — Vectors are (vectors of scalars) are “rank-1” — Scalars are “rank-0”… the pattern should hopefully be clear: A “rank-3” tensor is sometimes called a “Triad” and is a (vector of vectors of vectors of scalars)… etc. Anyway, tensors are a type of Sequence: 1) Tensors don’t have to contain numbers. 2) Tensors are Tuples (definite sequences: they don’t change size), which can be infinite or finite. 3) Tensors are Arrays (they have shape). The shape of a tensor is related to its rank; a “rank-N” tensor has a shape of N-dimensions. Ex1) A 2x2 Matrix has a shape of (2,2), has a size of 4 = 2*2. Ex2) A 3x4x5 ‘Triad’ has a shape of (3,4,5), has a size of 60 = 3*4*5. So, shape describes dimensionality (the examples are easier to follow). 4) Tensors are arrays belonging to an Algebra called “Tensor Algebra”: Tensor Algebra includes operations: “Scalar product / division”: (scalar * tensor = tensor’) “Tensor addition/ subtraction”: (tensor + tensor = tensor’) “Tensor product (called Tensor contraction)”: (tensor • tensor = tensor’). I would argue that the dot-product for vectors is a form of tensor contraction, that results in a 1x1 vector (which is basically a scalar); however, you can only get this result if you transpose one of those vectors, which is makes the argument fall apart. Tensors can be intimidating, but are pretty intuitive, once you get all of the important information. Important side notes: Tensor rank is different from the term “tensor order” — order refers to the number of dimensions greater-than 1, a tensor has in its shape: Ex) A 3x3 Matrix is rank-2 and order-2, while a 3x1 Matrix is rank-2 and order-1 (because this second matrix is basically a vector). Aside) Because we transpose a vector to do the dot-product, the vector is technically: A matrix of rank-2 and order-1,,, and not a vector anymore. Tensor contraction has some interesting rules for the resulting shape, ask chatgpt to describe it to you— but it is hard to wrap one’s head around. From a geometric standpoint: - Vectors and points are very similar. - Matrices correspond to an entire coordinate system of the space containing those points. You can plot tensors in a space, similar to points. This space is referred to as a “Tensor space”. A “Tensor field” is a common function (I think it’s a function, but could be wrong) for plotting the tensors in that space. This space is also often affine so it still has a coordinate system— which is wild. Cheers 17 Reply 2 replies @tomatochemist 2 years ago This saved my life, my graduate research project has unexpectedly involved learning to use tensors as a non-mathematician. Reply @xenmaster0 10 years ago Single best description of tensors I've heard, period. Why 27 components in a rank 3 tensor? Because 27 is how many items you get when you combine 3 things in 3 dimensions in all possible ways. 27 = 3^3. A rank 3 tensor combines all three basis vectors with all three indices in every possible way. Therefore a rank 3 tensor shows every possible force on a solid in 3 dimensional space. Any force on a three-D object will break down into some combination of the basis vectors plus the forces described in the indices. "Oh, so tensors are just matrices?" Not quite. Tensors have directions associated with each index, given by the basis vectors. You could say that tensors are matrices made of vectors. "Unlike a matrix, which can only represent a linear map between vector spaces once a choice of basis vectors has been made, a tensor is a linear (or multi-linear) map. The generalisation from linear to multi-linear maps is a distraction which may lead one to believe the difference between a tensor and a matrix is that a tensor is a generalisation of a matrix to higher dimensions, but this is missing the key point: the machinery of changes of coordinates, which is external to the definition of a matrix as an array of numbers, is internal to the definition of a tensor." -- Tensors and Matrices, Jonathan Manton's Blog, 21 October 2011. A rank zero tensor is a set of numbers, a rank 1 tensor is a vector, a rank 3 tensor is a linear map, a rank 4 or higher tensor is a multi-linear map. 71 Reply 6 replies @TrilokNegi10 4 years ago I enjoyed learning from this video. it is simply so immersive. masterpiece. Thank you Prof. Dan. 4 Reply @losthor1zon 6 years ago "Tenser, said the tensor. Tension, dissension, apprehension have begun!" (from "The Demolished Man" by Alfred Bester) 17 Reply 1 reply @jb______ 1 year ago Thank you for explaining in 12 minutes what I could not grasp in a full semester. Reply @LoonyLooners 9 years ago I'm quite impressed by how complicated everyone else has made it, having seen you explain it so simply. Thanks for this very helpful vid. :) 60 Reply 3 replies @avtaras 7 years ago Well explained, amazing content; crystal clear :) 5 Reply @iliketrains0pwned 4 years ago Thank you so much! I'm taking Advanced Aerodyamics and Aircraft Structures this semester, and it's my first time hearing about tensors. You really helped me intuitively understand what they are much more clearly than my professors could through mathematical proofs and linear algebra! 24 Reply 2 replies @jaredrego7642 1 year ago Thank YOU for your time. This is the best explanation of tensors that I've seen ! 1 Reply @serjerzemin 6 years ago What a great explanation! I appreciate it sir. 5 Reply @RaviShankar-im5zr 7 years ago Thanks sir l am a school teacher in India and first time I understand physical meaning of its. 10 Reply @michaelneedham6708 9 years ago Great explanation with illustrative props. The only thing missing is an example of how a tensor of rank 3 might be used. 19 Reply 6 replies @rohanphutke4999 1 year ago (edited) Most comprehensive explaination of Tensors ever, Hats off! 2 Reply @MsPreyashi 6 years ago Sir if I may say.. you are awesome... the way you've explained this is just so amazing... hats off!!!!!!! 6 Reply 1 reply @geoffwhite3664 6 years ago A brilliant use of manipulatives to explain a difficult concept. 18 Reply 1 reply @cutcc 6 years ago That shadow demonstration kinda blew my mind. Always thought you had to use computer graphics to showcase that =p. 34 Reply 1 reply @alexisrdevitre 1 year ago I only started to understand tensors after watching this video, many years ago. I still enjoy watching it when it randomly pops up on my feed. Reply @radwizard 8 years ago BRAVO!!! Right on! Thank you! Perfect! 5 Reply @ShaunAbdilla 5 years ago Thanks so much, Dan. You clearly have a good heart and an amazing talent at passing knowledge. 7 Reply @________6295 8 years ago a tensor is something that transforms like a tensor 18 Reply 3 replies @realpow3rs 3 months ago This man was born to teach. Thank you! Reply @islamiwzaif1691 7 years ago <3 I can't explain it in words simply: This the best tutorial I've ever had. 5 Reply @AlfredEssa 9 years ago This is a superb intuitive explanation of tensors. I also love your books. 14 Reply @ErkaaJ 8 years ago If you study mathematics, vectors are no longer objects with direction and magnitude. Heck, the magnitude is not even defined for vector if not a norm exists. 21 Reply 1 reply @lostzoro007 3 months ago That escalated quickly 2 Reply @viascience 9 years ago Excellent presentation! 15 Reply @oussamaali8393 10 years ago this guy deserves a nobel prize 6 Reply @StrangeAttr 11 years ago So a tensor is just an array of any given number of dimensions like a matrix is a 2D array and a vector is a 1D array? When we say about a rank 2 tensor component to consist of a surface vector and of a force vector is the forcr vector defined in the same coordinate system as the surface vector is or in the new coordinate system defined by the surface? PS: looking forward for a tensor field explanation... 5 Reply 1 reply @kevinedwards7079 2 years ago At 60 you have taught me a new mindset sir thank you Reply @tstratto14 6 years ago Vectors can represent area (with the magnitude being the size of area and the direction being orthogonal to the surface of the area). If you have ever been to college you can now skip to 7:48. 21 Reply 6 replies @ParasFtl 11 years ago higher rank tensors ie rank 2 tensor 8:45 4 Reply @borismezhibovskiy7607 7 years ago As a computer programmer, I understand vectors well enough to do lots of fun things with them. I still have no idea what I would use a tensor for, that I couldn't use a collection of vectors. 6 Reply 8 replies @carbodose 1 month ago My go-to video for tensors if anyone ever asks me to explain it. Thank you! Reply @shafayetshourov8268 2 years ago Sir, after watching this video, my perspective on vector has completely changed! 🤯 8 Reply @garystanley105 6 years ago Great presentation, but one key thing missing: examples of the use/importance of tensors in the physical world, esp rank 2 tensors like Stress, Strain and Inertia and possibly s rank 4 tensor like the Constitutive tensor relating Stress to Strain. It would be natural to introduce force vectors (rank 1 tensors) as well as your area vectors and then note that stress is defined as force per unit area, hence the need for a rank 2 tensor to fully describe the state of stress at a point. Another helpful perspective might be to connect rank 1 tensors (vectors) and rank 2 tensors to 1d and 2d matrices, respectively. Since people learn differently, adding examples and alternate ways of looking at the same (initially) abstract thing would increase both motivation and comprehension — or at least curiosity to look more closely — for this often overlooked subject, and benefit a wider audience. In summary, if you were to add 3 minutes of cool examples and a mathematical glimpse, you might produce the first viral video about Tensors on the web (IMO). 174 Reply 14 replies @jacksainthill8974 9 years ago Tensor very much for the lecture. :) 7 Reply @StupidSheepenio 3 months ago Holy, this is the best explanation for what is a tensor I've ever seen, I finally understood Reply @Kong9901 8 years ago what's the difference between a tensor and a matrix ? 10 Reply 4 replies @chrisofnottingham 10 years ago IMHO, the background is familiar and takes for ever, and the key new idea is rushed through at the end, leaving me very little wiser. But I guess I now know it is to do with coordinates and vectors. 202 Reply 16 replies @marcostavarez2702 8 years ago I'm guessing this is very useful in fluid mechanics 5 Reply 1 reply @koulickchakraborty8498 2 years ago You're out of my tiny words of thankfulness. You're the best one to explain this Reply @BarriosGroupie 9 years ago "All observers agree on the combination of basis vectors and components". I still don't understand what he means by this. 8 Reply 3 replies @prakharasaiya5002 8 years ago Just a question, he said in 11:32-11:36 that all observers in a reference frame agree. They agree on what?? 7 Reply 4 replies @PhilippeCarphin 10 years ago I feel like if you're wondering about tensors, then the first half of the video is a given. 235 Reply 10 replies @JohelSouza 10 months ago The good old days of YouTube. I really miss that. Reply @שלומית-ק9ה 7 days ago Best explanation . 14 yrs and ppl and , still, students r learning from you. I Reply @SmickEDibbly 2 months ago (edited) I'm a 34 year old PhD candidate in mathematics and everything past 8:20 was extremely helpful and new to me Reply @PlasmaCoolantLeak 2 years ago (edited) The mark of an expert is someone who can explain a difficult subject using simple objects. Dick Feynman did it with an o-ring and ice water, you're doing it with kids' toys. Well done, sir. 2 Reply @SuryaUday20 2 years ago (edited) In understood this 11 years later after watching it many times when I really paid attention and felt the visualization internally. The video deserves an Oscar! 2 Reply @KaniSha-b7x 4 months ago I already knew what tensors were and there uses, but I still learned something. Thank you Doc. 1 Reply @alejandrourielgomez4714 2 months ago "All observers in all reference frames agree, not on the basis vectors, not on the components, but on the combination of components and basis vectors." Gold. 1 Reply @geekionizado 11 years ago This video begins with a long explanation of something really easy, and then suddenly presents tensors without any motivation for the creation of such structure. In fact, this video only helps to visualize a tensor, but gives no details of its advantages and uses. 33 Reply 7 replies @baekbeomchoi6716 1 month ago I was struggling to understand the difference between GPU and TPU and this video helped a lot. Thanks for sharing this sir! Reply @patvdp6754 7 years ago Ok so ... what is a tensor ? 73 Reply 11 replies @AlphaKnight007 5 months ago This is the best explanation of tensors and vectors i found on internet, hats off to you professor dan fleisch Reply @almendronman 2 months ago You know when someone knows his thing when he can explain it without gibberish neither fancy words! Thank YOU professor! :D Reply @youtubetest3770 8 years ago So a tensor rang I will be a vector ? 9 Reply 2 replies @suave319 7 years ago khamponent 21 Reply 2 replies @hernandariobernalparra7772 3 months ago Best ever video about what tensors are! Reply @PhysicsMathMan 10 years ago very fun and well spoken 9 Reply @corey333p 8 years ago What syllable should I stress in the word "component"? The first or the second? 4 Reply 2 replies @HeyItsSahilSoni 8 years ago That "Thanks very much for YOUR TIME" earned my like! Nice work Sir, keep on doing such great work 😄 5 Reply @fatkraken3140 6 years ago i swear if teachers were this cool in schools everyone will end up with a phd in physics 5 Reply 2 replies @mobili2 2 months ago This is just beautiful. The simplicity you managed to bring to these mathematical objects is outstanding. Thank you very much and may God bless you Reply @ophello 7 years ago I still don’t understand tensors. 19 Reply 7 replies @Snails6534 2 years ago 2023 and I cannot tell you how much I needed this video. Visual representation at its finest. I’ve been trying to wrap my head around machine learning but could get tensors. Reply @flupoop 11 years ago Your last name means "meat" in German. 8 Reply 1 reply @SameerBatt 8 months ago Halfway through this video and smiling on the fact that how fantastically a concept can be taught. Reply @parithimathi 2 years ago மிக மிக அருமை ஐயா. மூன்று அச்சுகளுக்கான மாதிரி மிகவும் சிறப்பாக இருந்தது. டென்சர் குறித்த விளக்கத்திற்கும் நன்றி. 6 Reply @TebiByyte 11 years ago Oh, so tensors are just matrices? 17 Reply 21 replies @NOSLIWKR 6 months ago Now I understand "tensors". Unique presentation. Bravo! Reply @Teddy0567 9 years ago I don't understand, how can an area-surface be represented as a vector? I understand how a force can be drawn as a vector and any combination of forces can be simplified to a net-force. But why would one draw an area-surface as a vector? Even tho this confuses me the video served as a great introduction and i have a better general idea. Thanks! 4 Reply 3 replies @farzanroshdieh698 4 months ago Beautifully demonstrated and explained. Reply @mathewmcfool 6 months ago I wandered in here looking for some help on this thing called Tensor. I came to the right place, thank Mr. Fleisch. Reply @Batman-n1q1v 1 year ago I have no need to learn about tensors but felt I had to watch this whole video to learn something new. Great job! Reply @meow75714 2 weeks ago Still loving this guy. Reply @lewis72 2 years ago As a food service worker at KFC, this is one of the best simple explanations for a tensor I've ever seen. Reply @gutzimmumdo4910 2 years ago wow the insight of vector representing an area. 1 Reply @ChemDamned 2 years ago I'm literally in awe. Thanks for existing. Reply @mediapc4747 2 months ago Explained so clearly that I am now worried about myself for still not understanding. Reply @stev2718 4 months ago Wow! The idea of a vector representing an area is a perspective that gives great insight (and vice versa). Reply @atudarden342 1 month ago I just watched your video and I will watch it several more times to get it rock solid in my brain, but this is the most simplistic and elegant explanation of what I’ve been struggling with in understanding what a tensor is. Again, Thank You!! Reply @hungariankid2112 2 months ago Wish this was reccomended when I was in college Reply @abdelrahmanashraf7636 2 years ago That is the best yet innovative way to explain Tensors on the entire internet. Thank YOU Mr. Fleisch <3 Reply @michaellucas7177 1 year ago Great explanation. Very concrete. Very plain. Very understandable. Reply @filipecanzi 2 years ago Before you started talking about Tensors, I already knew this was a fantastic video! Thanks for sharing! Reply @puneetmishra4726 1 year ago Thank YOU for your time, Dan. Reply @nexp2845 5 months ago One of the most educational videos of all time. I wish institutes would take reference to this video at the start of the VECTORS class. Reply @arthbarros 2 years ago (edited) This was the shortest 12 minutes of my life. I really enjoyed this video. Reply @ermaolaoye 7 months ago If I became a teacher in the future, I definitely will show my students this video to teach them vectors and tensors. Reply @StatsScott 2 years ago I’ve watched a number of videos on physics and relativity and this is by far the best explanation of basis vectors and tensors I’ve seen. Reply @wasp626 6 months ago Considering this is a 13 year old video, the way you "practically" teach complex topics is amazing. I can tell you must have authored some amazing work in your time. I am subscribed and following you now. Reply @jimmyniland9721 2 months ago Can you imagine if every child and older student was taught by someone like him ?! I wish that I at any age had had a teacher like him. Reply @derekkuhl 4 months ago Not being a mathematician or physicist, I didn't know that I needed to know about tensors. But now I feel like I have a reasonable understanding. As others have said, this is a master class indeed. Reply @Nsimalen 1 year ago After watching several popular videos about tensors without understanding them, I finally did it with this one. Just FANTASTIC!!! 👏👏👏 1 Reply @ImRupeshBadgaiyan 2 months ago Beautifully explained Reply @sabbirazim1221 2 months ago what an explanation! This just nudged me to start schooling again under your supervision! Reply @RAPHAELMATOSDASILVAGONCALVES 1 year ago Thank you so much! You're the first who made me understand tensor ranks! Reply @jayasuryanarayanapodipired6008 9 months ago Loved this to the core SIR!!! , I bow to you for your patience and passion Reply @MamToCos 6 months ago Dan, well done 😀 Thank you.👍 1 Reply @Casey093 2 years ago It is a pleasure to see a teacher that has an interest in passing on his knowledge and won't just scroll through 50 slides of differential equations copied straight from a book and call it a day. Reply @tea00wizard86 1 year ago In all honesty, I miss read the title as "what's a tennor" and I assumed this video was about singing but this was way more informative than you could ever imagine. I'm currently 17 and a grade 11 learner who's physical sciences' marks suck. I haven't had the best teacher so I've had to teach myself about vectors and I realise it's not a difficult topic but I really struggled and still do. The way you taught through this video really inspires me, it makes me feel like I have the ability to understand these topics and more. Recently I missed a huge opportunity that I felt could've really changed my life and I've been battling to pull myself up from my lows especially with the low marks but you've given me a different type of motivation that I really needed and appreciate. So thank you Dan 1 Reply @capry6565 1 year ago Brilliant! I wish I had teachers like You in my childhood Reply @vintagejock3951 2 years ago This is one of the best videos regarding vectors Reply @Ab.Stat. 2 years ago Remarkably resourceful use of props, wonderfully illustrates the points as he is making them Reply @sethrodgers552 2 years ago Wow ! Very nicely explained. Bravo 1 Reply @TurtleMonster-f9o 2 months ago This is pure gold. Thank you so much!!!! Reply @LawandOrder-y4c 9 months ago The significance of tensors at the end was a crucial part of the video Reply @kunalkolambe4414 5 months ago Thank you for explaining in an easy way...🎉 Reply @chirayubhardwaj4608 5 months ago Great explanation!! Beautiful visualisation Reply @cecilswenson3162 6 months ago When I saw the thumbnail for this video, I thought, “N.T. Wright does physics too?” 1 Reply @alanstarkie2001 1 year ago Brilliant way of explaining these concepts. Reply @rio_agustian_ 3 weeks ago Thank you for your explanation! Reply @vivekbadami8053 9 months ago I love this guy - so generous with his time to provide such a beautifully simple explanation of the basics of tensors. Reply @bynonn 2 months ago Thank you for your clear and enlightening explanation. Reply @pimbu936 8 months ago God tier educational value here Reply @Krv2001 2 years ago You should be in the teachers hall of fame, if there isn’t one, let’s create one and put you on that. THANK YOU FOR YOUR TIME, SIR. Reply @jayhu6075 2 years ago (edited) The best explanation about Tensor. Everybody in the world must go to this channel to understanding this topic. Reply @peterbutler5597 1 year ago Thanks for the Lillian Lieber reference. More exploration in sight. Reply @freedyferem 7 months ago Prettiest video I have found on youtube. Loved every second Reply @faiyazsakib7620 2 months ago oh, the rawness and ogness of this content.... Reply @iangallimore4474 11 months ago Thank-you I had heard a friend talk about the tensor when discussing his Physics studies almost 60 years ago, and this has been very helpful! Reply @MKultraplus 9 months ago (edited) This video has almost 4 millions viewers All your Other video have less than 1 per cent of this amount viewer ! It Means something Please Do more amazing explanation video like this one 1 Reply @LupinoRajabi 2 years ago Just wanted to say thank you for making maths and physics fun and interesting:) Reply @markr9640 10 months ago It's the 3rd or 4th time I've watched this. Pure genius. Thank you. Reply @tusharjain9366 2 years ago One of the best explanation of tensors Reply @tony_longson 10 months ago I love how he says "a point'ed stick" like Eric Idle! 1 Reply 1 reply @richadutt665 1 year ago Thank you so much. This is best explanation of tensors I have seen so far. Reply @josemanuelquevedovargas9613 11 months ago Literally the best explanation i've seen so far. More teachers should learn from him to put complex things to a simpler level Reply @SaiGollapudi-f1w 2 months ago Thank you sir for your great explanation. Do keep them coming. Reply @saveriogz 2 months ago really hope this guy is doing well, thank YOU so much! Reply @neelamberbanik8958 1 year ago I am in class 10th and this video is so incredible that it even made it easy for me these type of teachers are the ones who truly love physics Reply @shobhitsharma584 2 years ago Thank you Dan Fleisch for such a great video Reply @girikkhullar4072 1 year ago Thank YOU very much for your time to create this terrific explanation of tensors. Reply @Paki_in_Indonesia 2 years ago Best Physics Explaination I have ever seen... It's not just making us imagine but visual explaination we could ever get... Thank You for this video... Reply @h0stI13 1 year ago This is the video that helped me break the ice in my struggle to understand tensors. Thank you so much! Reply @leandromfm 1 year ago I just got my mind blown away. You're insanely good with teaching!!! I need to share this with the world!!! Reply @solomondawit8866 1 year ago Your in-depth knowledge of the subject made this complex topic so simple that even grandparents could understand it. What a masterpiece! Reply @N0Xa880iUL 3 months ago You've done your best 13 years ago without the now ubiquitous animations. But I think the part after 8:00 could very well do with some nice animations 1 Reply @SidGoodOldDays 11 months ago Thank you very much for your efforts! What an educator you are! Reply @SirFartsAlot42069 2 years ago I don’t know why this was in my recommendations, I’ve never watched similar videos. But I’m glad it was! Reply @wolfgangmorgenstein2289 1 year ago THE BEST EXPLANATION OF TENSOR FOR DUMMIES. THE VIDEO TITLE MUST BE TENSOR FOR DUMMIES. THANK YOU SIR. Reply @mvmcali6900 4 months ago I love the effort and sincerity that this guy put into this quality effort . The fact that it is so old school … with physical items arranged on his dining room table rather than AI or fancy graphics makes it feel endearing… like we’re are witnessing the transition between two eras of humanity. I hope this guy is enjoying his retirement. He should feel very satisfied that he educated a lot of students through the years Reply @rajendramisir3530 5 months ago (edited) Thank you for your time and effort, Professor Dan Fleisch. I took notes while enjoying watching your video on Tensors. A well explained and patient demonstration to build and motivate intuition for Tensors. Amazing facts of the Universe as observed in the quote you mentioned. Reply @mjp152 2 years ago This is better didactics than 99% of the stuff I was subjected to in my engineering studies. Reply @MrAmyiro 2 years ago Thank you very much Mr. Fleisch, this is the best explanation of what is a tensor I've ever seen ! Reply @_sh4512_ 2 years ago This is one of the best videos ive ever seen in making complex maths easier to understand. thamk you for your time Reply @martinfiedler4317 2 years ago Only found your video by "accident" due to the YT-algorith. Thanks for YOUR time and effort that went into it. It is an exceptionally good educational video! Reply @fourfoldway 2 years ago This was a master-class in explanation. Brilliant. Reply @yodaheyohannes2776 6 days ago Brilliant explanation, thank you sir Reply @randomshorts-ks7dw 2 years ago Watching this masterpiece after 11 years ♥️♥️ Reply @NitishYadav-nc7tw 2 months ago Thank you so much to explain it so nicely I wish I had teachers like you so passionate Reply @myownspace931 3 months ago Thank you sir for your time. What a great yet simple explanation. Reply @Kiffikiffe 1 year ago I think it's almost impossible to explain it better 1 Reply @nugrahal7208 2 years ago thank you, I just learned Tensor from online course, and they brought me here. amazed with this videos view and like numbers 1 Reply @karoinnovation1033 11 months ago Thank you Dan, for your time. Such a great video. Reply @arush_chinchkhede 2 years ago 9:14 is the best thing happened in my life. Thank you very much sir. Reply @Shocker99 2 years ago You are a great teacher. I would have loved to see other things explained by you. Reply @aurinator 1 year ago Great explanation!! Fingers-crossed a similarly good one for Fourier Transforms will eventually follow... :) 1 Reply @UweSeelerTheGreatest 2 years ago Better then every explanation in the university - if they ever tried it. Thank you very much 🙏❤️ Reply @ianogard 2 years ago Thanks, Mr Fleisch, for simplifying my understanding of certain variables in equations that I've been wrestling with for years. Reply @shanusays 1 year ago I worked out tensor maths in engineering college, but understood fully now Reply @testrabbit 4 weeks ago 👍🏽👍🏽 really concise explanation! Love it. I'm going to rewatch it with my daughter. Reply @RossEthridge-q7u 4 months ago Amazing explanation. This helped with my PyTorch class. Thank you! Reply @nirmalyasarkar6426 1 year ago Sir, I am not a student anymore, still just watched the entire video, thank you! thank you for doing this for all students.....this is probably the best explanation of tensors on YouTube! I wish I found this video in highschool 😅 Reply @xyzbesixdouze 2 years ago Much respect, and thank you for spending your time educating us. Reply @fredericoamigo 11 months ago Absolutely beautiful, brilliant and wonderful. This guy is in a league of his own! Reply @philosopher_sage_07 1 year ago (edited) Thank you so much for taking the time to do this beautiful explanation. These are times that make me glad that I chose the field I did. Tensors are indeed facts of the universe. Reply @SuperMakoto13 2 months ago Fantastic explanation! Thank you so much! Reply @IlIlllIlll 1 year ago Very well explained! 1 Reply @shravanap828 2 years ago face-red-heart-shapePractically explained in a concise manner Reply @franciscobolivar373 2 months ago Dr. Fleisch, you are OUTSTANDING at teaching. I didn't study tensors, but I wanted to know what it is since I knew that permeability of a rock is one of them. I read some about it, just a lot of matrixes didn't get it. I watched a video recently too and I understood what you said at the end about different observers see same tensor, but now I really know what a tensor is. You explained as we were 5. Thanks a lot for your effort in preparing all that stuff and the explanation. Reply @GromPilot 1 year ago (edited) This video is well crafted. I remained engaged throughout. Thank you. Reply @mtyson123 5 months ago The parenthesis moment is really something. Reply @MrBendybruce 2 years ago This guy was born to teach. Reply @cjk9988 2 years ago One of the best videos on Tensors, no complicated animation and none of the vague jargon. Thank you for making this video! Reply @mohammadkermani2987 2 years ago Thank you! It was very straightforward and creative! I liked how you switched camera position in order to make things clearer to understand Reply @Glademist 2 months ago Thank you Mr.Fleisch. Reply @cifey 6 months ago My house nor my mind has ever been that clean and organized. Anyway it would be interesting to see these vector components in use in super dimensional math. Reply @Solomoon-l7m 2 weeks ago Thank you for this informative video Reply @ahmedfarag7138 3 months ago Thank You, Brilliant and simple explanation. You blow my mind Reply @alikurtulan6621 2 years ago I could be a math professor if I could have lecturers like him Reply @StarTheExplorer 2 months ago Oh man that was the great explanation. Thank you Sir. Reply @abwuds7208 2 years ago Your voice is so good! Had some ASMR vibes while learning something really well explained and interesting Thanks for your time! Reply @larrygoodman2442 1 year ago Thanks for this video! I wish my physics professors had used your system to explain vectors in class. Reply @tubeasjay 4 months ago i wish i got enough background in physics to follow along. i am very certain he did so much justice explaining tensor right here, literally the cheapest explanation anywhere. Reply @Beatsymphony411 10 months ago As a high school student, I can confidently say that I finally understood what a tensor is and how it can be applied, thanks to this video. It really helped clarify the concept for me! Reply @user-tg2oi2ey7w 2 months ago Thank you so much. Your explanation is the best. Reply @captaindragon8179 2 months ago This is brilliant! Thank you! Reply @TheAmbientMage 2 years ago That was pretty well explained and really straightforward. Thank you. Reply @pranavkumar6418 1 year ago Was doing a ml course and wanted to know about tensors, henceforth clicked on this, worth every second of my time Reply @1ProsperousPlanet 1 year ago Now I finally understand Einsteins Gravity tensor. Thank you so much. Reply @SyedAsad78 1 year ago A born teacher, if ever I saw one! Beautiful explanation and it is still relevant in 2024. Reply @saboo480 2 years ago As a random guy that doesn't do any math day to day but finds it fascinating, I absolutely loved the care and and time you took to making this video. Thank you so much! Reply @fahadelahikhan 1 year ago @DanFleisch I am watching this in July 2024. It helped me a lot understanding tensor (a better visualization about tensor). I am really glad that youtube suggested this video. Thank you sir. Reply @FearNoNumbers-y3x 1 year ago You sir are very cool! And your clarity is so coherent that any of my middle school Algebra I kiddos could follow you. Your use of manipulatives and models are stellar to build strong conceptual understanding. You didn't first resort to expressions, equations, and formulas. You just sat us down and coached us. Reply @albe2478 1 year ago ty mr. fleisch! i very much appreciate your time and willingness to explain this. Good man! Reply @yuvrajwankhede8083 2 years ago That was an amazing explanation. explained so easily. Thank you Mr Fleisch. Reply @Heinz916 2 years ago Salute sir. As a matter of fact this short video is a master piece. Reply @Scarlettneo 1 year ago Loved it professor! Thank you on miles! Such a treasure Reply @realdragon 2 years ago That's extremely well done, everything is explained step by step building up to explaining what tensor is Reply @AyzahGardezi 1 year ago Why couldn't I have been recommended this BEFORE my Deep Learning course ended T-T Reply @WalterScott-t9z 2 months ago That was such a good lesson. Reply @sneddie 2 years ago Hi Dan, just finished watching your video and wanted to say thanks. Excellent explaining! Reply @elhadjiousmanediallo1618 2 years ago Thanks Mr. Fleisch👍 1 Reply @matthaitm8945 2 months ago Excellent explanation Sir. Thank you very much. Reply @AliBinyusuf-n4f 1 year ago (edited) Many thanks for the great explanation of vektors and tensors. Again many thanks. Reply @JonJenkins1982 2 years ago Around 7:27 I started flashing back to my 3D programming lessons where I had to do matrix multiplication with vectors Reply @romans595 11 months ago Best professor i ve ever heard Reply @diegomasone 3 months ago Great video! Thanks. Reply @phillysheem99 2 years ago It’s pretty straightforward 😂 1 Reply @pkmpkm03 1 year ago After years, now I truly understand tensors! What a beautiful, concise, even paced educational video. And actually, THANK YOU for taking your time to create this video. I hope you are happy and in good health.....:) Reply @FranzStFleur 1 year ago (edited) Great video thanks for using simple visuals Reply @ericip778 6 months ago Thanks for enlightening me. Thanks Reply @herohero-fw1vc 1 year ago Excellent introduction to tensors......and very important concept. Reply @QamarRaza-e7z 6 months ago thats really amazing way of teaching, love it Reply @syncronic 2 years ago Dr. Daniel A. Fleisch deserves immense praise for his incredible talent in explaining the concept of vectors as the foundation for tensor compression. His clear and concise approach makes this complex topic easily understandable, allowing both students and professionals to grasp the intricacies of data compression with confidence. Dr. Fleisch's ability to break down complex ideas and present them in an accessible manner is truly impressive. His passion for the subject shines through in his engaging explanations, making it easy for anyone, regardless of their mathematical background, to follow along and grasp the essence of the topic. I am grateful for Dr. Fleisch's dedication and his exceptional ability to make the concept of vector-based tensor compression come alive. Dr. Daniel A. Fleisch is an outstanding educator when it comes to explaining the concept of vectors as the basis for tensor compression. His approach is both clear and concise, enabling a deep understanding of this challenging subject. I am truly amazed by his ability to make intuitive analogies and connect key points, making it accessible even to those without advanced mathematical knowledge. Dr. Fleisch's passion for the topic is contagious, and his unwavering dedication to making the content accessible for all is truly admirable. I am thankful for his contributions in simplifying such a complex concept and for his exceptional skills as an educator in this field. Reply @muon537 2 years ago By far, the best abstraction of a complex subject explained with such simplicity should be the base for every introduction to engineering class. Thanks for your wonderful explanation. Reply @feywer 1 year ago Wow! I heard an experimental audio cassette months ago that had sampled this man’s talking and didn’t know what it was from until I stumbled on this video - random! Cool. Wish I could recall the tape. Reply @sebadb6037 2 years ago for so long i've wanted to know what tensors are, and this video is just what i needed. thank you so much Reply @viveksingh5528 2 years ago (edited) Sir for us students you are a GOD. Thank you soo much in taking much effort to teach us like a junior grade. Leaning becomes fun just because of teachers like you. thank you once again. 1 Reply @Seaserpent-m8n 1 year ago These UTube “classes” have taught me in a more understanding way than i ever could learn in a high school class by teachers just talking Reply @culturedgator 2 years ago You are a blessing. Thank you for your time. Reply @BigBrother4Life 2 years ago Best best video ever on tensors and vectors. Reply @SouravKumarMoyra 2 years ago I can't belive that Without Any animation.....He teaches this with so clarity 😍😍🤩🤩 Reply @231ujwalvarma2 2 years ago Wow! i finally understood this after 4 years Reply @SohelRanaSarkar-j2v 11 months ago I really want to thank you from my heart. Reply @MariaBug 2 years ago I’m learning python and ML… and this video is the best explanation to understand TensorFlow! Thank you, thank you, thank you! Reply @noahwinslow2692 11 months ago I absolutely love that this man enjoys explaining things to people so much, that he took the time to arrange nerf darts and wooden blocks to explain something pretty complex for people who may be struggling to visualize it… Thank YOU for your time sir! Reply @dep7311 2 years ago Thank you for sharing your time with us, Sir😊 Reply @lalalanding234 9 months ago Thank you for going out of your way to explain a highly theoretical topic in such a tangible way! You've brought maths alive. I find theoretical topics hard to apply to real world. But you made it easy to understand. Thank you so much. Reply @kanugupta1044 5 months ago Woww!! So So So wonderful video and so relevant still even after 13 years!! Hatsoff to the greatest teacher! Felt like even a class 2 kid would understand this! Reply @d_a_k_s_h_17 2 years ago thank you so much sir!! this vid is a gem for anyone starting to understand vectors. it provides all the necessary visualization to proceed. Reply @LionOwono 1 year ago Thanks to you for taking this time Reply @PANDURANG99 1 year ago 12 years ago , there was a tensor consept amazing 🤩 Reply @AnmolSharma-ij1ut 1 year ago it was literally a great explaination that could be possible for the tensor Reply @adamsun1050 1 year ago So powerful and easy to understand . Thank you so much Reply @flikkie72 2 years ago Saw "tensor" and thought that I should know more of those with google's alphaTensor being a thing now. Wasn't expecting this lovely explanation Reply @demetriusjohnson5358 2 years ago this guy, is legendary. Legend has it, that his basis of intelligence was from a component never to be seen in man again. Reply @jameswho5517 1 year ago Best explanation, thanks for making this so clear and easy to remember, subscribed. Reply @Michael-iw3ek 2 years ago (edited) Tenser, said the Tensor. Tenser, said the Tensor. Tension, apprehension, And dissension have begun 1 Reply @enessahin769 2 years ago you are a great teacher, sir. Thank you so much for sharing this lesson. Reply @taherjijel518 3 months ago Appreciate your efforts. Really a good nice explanation. I never took tensors at university. Thanks a lot. Would have been a pleasure to meet you in real life. Reply @VolSacks38 11 months ago I still don't understand when you would need a Rank 2 Tensor to describe a force on a body. For example, look up a stress tensor...how does o33 differ physically from o23 or o13? Aren't they all forces that are pushing up/down with the same magnitude, no matter what plane (x,y,z) they are pushing against? In other words, how could the force in the z-direction on an xy plane ever differ from the force in the z-direction on an xz plane? I just don't understand how physically this would look. Does wind not shear in the same direction & magnitude at one spot no matter what plane it is shearing against? 2 Reply @rejoanbary2155 2 years ago This video is helpful in learning about both vectors and tensors. Reply @rubncarmona 2 years ago if it wasn't enough to present us with a delightful good paced explanation, he also ends the video with a bomb of a quote that helps you both internalize the subject and also feel more curious about it. Thank you! Reply @ambu.6707 1 year ago crazy how much conceptualizing slope as ‘rise over run’ in like 4th grade prepared me to understand and process tensors. i got my beef w descartes but he did kinda cook w the cartesian grid Reply @arriamirorei1925 1 year ago This is the best explanation of what a tensor is that has ever been made. An absolute marvel, thank you very much! Reply @mredafamily 6 months ago Thanks Sir! Very well explained! Reply @Ranveer-j6u 1 year ago Great Video for introduction to Tensors. Reply @goffakten1953 5 months ago I've been sending this to people I work with who say that can't "understand ML papers", and otherwise are masters or PhD. level or more in bio, etc.Turns out the math isn't that hard and this tutorial is all they need to understand what effectively amounts to notation. I've done this many (10+) time with full success, to the point that it's stickied! Thank you so much, Dan. Reply @nafeesashaik5778 1 year ago Wow what an explanation sir !! 👏👏 Reply @lakshveer07 2 weeks ago WAOOO THE AMOUNT OF WORK HE DID TO MAKE US UNDERSTNAD T~Tthank youu Reply @uddiptalukdar 2 years ago It was so serene and beautiful! Reply @dragweb7725 3 months ago (edited) actual incredible explanation, i finally understood the background of this object i've been using in quantum chemistry everyday while brushing it off as "it's simply a matrix, why use another word ?" but actually, while a rank 2 tensor coefficients can be represented inside a matrix, the actual concept is so much more general than simply its representation in a 2D array, and really not that complicated with your clear explanation, thanks a lot ! Reply @1ProsperousPlanet 1 year ago This was great, I really enjoyed your no nonsense approach. I hope you are still doing these videos (I just found your channel(It was just in my feed)) Reply @nat3llite 2 years ago Thank you for making this video. Excellent explanation. Reply @redsix5165 2 years ago I was watching a series about general relativity- this really helped make sense of what a tensor represents!! Ty!!!! Reply @TamasDrNagy 2 years ago a real TEACHER! Congrats Reply @Eric06410 3 months ago I need this guy to be explain a twister to me Reply @ParallaxParadigm 2 years ago Beautifully explained..👌👌🙏 Reply @TheBlackhorndown 2 months ago Thanks very much for your explanation, good sir. Reply @wanderfra42 2 years ago The "some" at 5:50 triggered me "All Stars" by Smash Mouth. :D My neural glitches apart, great great video!! Reply @SuperSurreal 1 year ago This was tremendously well explained! I really appreciate the effort you put into carefully crafted and setting up these visual explanations. You made this concept very approachable for me and I understand it now! Thank you! Reply @ozanmuyes 1 year ago Remarkable effort! Thank you! Reply @johnschuster4287 1 year ago Thanks Dan. Thanks for putting in the work to help folks understand the visualization of tensors. Every instructor of such should have to use this video/ If you were to expand on your presentation to upper level physics students, you might include time and the use of the word metrics. Reply @DelorianTracking 2 months ago Thank you! I love how you make tensors intuitely make sense geometrically. Very very helpful. I only wish you had similar vids to spinors and spinortensors 😅 Reply @marksmith1824 1 year ago As a Physicist with decades of experience (PhD in the previous millennium 😂), thank you for this accessible explanation. I wish this had been available when I started learning about tensors. Reply @CyberSystemOverload 2 years ago Why do people thumbs DOWN such educational content? What is wrong with some people? Were they expecting TikTok selfie dance? Awesome video Sir! Thank you! Reply @SanchitSingh-x6s4r 1 month ago Damn!! I wish I had you as my Physics Professor! Reply @OlympicMaths 6 months ago I really love your video, sir. Reply @Atjayvang21 1 year ago Thank you for taking your time to share and pr pass on knowledge. Reply @devarshibrahmakshatriya8710 1 year ago Thank You for your time. Reply @Prof_Nazir_Ganaie 1 year ago His book on vectors and tensors is a conceptually rich book Reply @kyleward5249 4 days ago I love how the attempt to explain the theory using real objects helps simplify for some and yet exposes the empirical truths which are in contention with theory. Mostly because the real objects help us understand deviations from the theory. For instance in the example by explaining the value in each coordinate by using a light source you expose the perspectival nature of reality (in opposition to if you could make the light abide by parallel projection and thus abide by Euclidean geometry) as well as ignoring relative gravitational effect on light. But non-the-less you are helping many to see the meaning of a tensor in at least your correctness. Reply @loversoul8206 1 year ago Thank you, sir. Live a long and happy life, best regards!! Reply @chemistrychamp3369 2 years ago I saw your video twice: once before reading your book and once after. I can only recommend to read your book it give great explanations and is easy to follow! Thank you Dr Fleisch! Reply @OvidiuRotaru-b6j 2 years ago Thank you very much,I finally understood what a tensor is. Reply @mayureshkarjavkar13 8 months ago Teachers like you are literally hard to find whether online or offline, Sir, your teaching is literally amazing and out of the world, just no words sir, you really cleared out my doubts and questions on tensors, thank you so so so so so so so so so so much sir ❤❤❤❤❤❤❤❤🥰🥰🥰🥰 liked and subscribed your channel!!! Reply @jurgendeleye6813 1 year ago Thank you for your time! Reply @leonidtitovcs5026 8 months ago Great job, very talented! Thank you! Reply @sakukullberg2697 2 years ago Tensors are always explained in such a complicated way. Reply @catalinatoledo8458 1 year ago Thank YOUUU! Truly appreciate to can watch this. Such an amazing teacher Reply @kaankaral 2 years ago thank you sir. Long and healthy lives. Reply @subhros_story 2 years ago I am in love with the video at first short. I completely love how it was taught. Could not express in words, Love from India Reply @mehmetdurna3115 1 year ago 3-4-5 triangle! I remember this from my childhood:-) Thanks prof. Reply @linusdeluca-perry7944 2 years ago This was really well explained and very helpful. Thank you! Reply @mathtonight1084 1 year ago This was a lot easier than learning about tensors from Roger Penrose... Reply @ericcestero2666 1 year ago Reminds me of Mr Wizards World of the 80s, the whole reason why I have been working in STEM for 28 years. Excellent explanation. Reply @akhkandimath 1 month ago thanks for your time Reply @hak14971 11 months ago The conclusion answers the videos topic question in a single sentence. Quoted "Tensors are the facts of the Universe" Brilliant video, thank YOU. 1 Reply @mostafasamir9472 1 year ago Thank your for your time and effort for making such a great video Reply @mustafaseval2733 2 years ago greatest explaination of tensors ever !!! Reply @martinledesma7926 1 year ago Thanks for your clearly and easily explanation. It was quite useful to me. Reply @VENKY-q5q3s 7 months ago Legend, Thankyou for your mighty lecture on "facts of the universe". Reply @mantidream8179 2 months ago This guy was clearly born to teach Reply @jbeaudin2 1 month ago This is amazing. Reply @manavgupta8484 2 years ago You are an awesome teacher. Reply @apar3258 1 year ago Great explanation. Thank you sir! Reply @mr2octavio 2 years ago I dont even know what a tensor is, probably heard them named from TensorFlow, but today i get what they're for. Thanks sir Reply @cyrusdeng0108 1 year ago this video make me first time to know about tensors Reply @simranjoharle4220 2 years ago This was extremely helpful! Thank You! Reply @datawithmans 1 year ago what an amazing teacher! Thanks! Reply @hareecionelson5875 1 year ago the permanence of tensors makes me feel at ease, they're the opposite of a hallucination: everyone can agree the tensor exists. The components may differ, but the total contents is absolute. Reply @christopherphillipson3083 10 months ago (edited) Thank you Professor for this. I also have your student's guide to Maxwells Equations which I am ploughing through - an excellent guide. Reply @omerfarooq0 1 month ago As a physics and mathematics enjoyer, from 11:33 onwards I legitimately felt enlightened, even though I didn't fully understand what he said Reply @parashar1505 8 days ago this is the best example of - "much ado about nothing"! Reply @pb4158 10 months ago Excellent attempt at explaining. But I did not understand many things towards the end of the video. What is a reference frame? What observer? 1 Reply @smzaidi1946 1 year ago Thanks a lot sir. You have explained it with so much effort. I am just commenting to appreciate your efforts and teaching thanks alot again. 1 Reply @lionelobaidur7961 6 months ago Didn't even realise it's a 13 yrs old video. 2 Reply @alexdev404 3 weeks ago 0:28 - The way he said "A pointed stick" just caught me off guard i dont know why 😭😂😂 Reply @marcelobr327 2 years ago Amazing lecture. I never thought understanding tensors could be so nice and easy. Thank You Professor Fleisch!!!! Reply @philippkistler1430 3 weeks ago I really enjoyed the literal projection by the lamp and keept wondering if the rays from the light bulb are perfectly parallel. Reply @chillbeach7322 1 year ago Clear and elegant explanation. I wonder if people realize how profound and impactful this knowledge is to advance our civilization into a new era of prosperity and peace. I am very grateful Mr. Fleisch. Reply @ManishSahu-t4g 5 months ago It was such a great video I got a really clear and visual understanding of tensors and the explanation was also so simplistic yet informative. I am so glad I watched it Reply @Joevega2962 2 years ago Thank you, @Dan Fleisch, for such an easy and imaginative explanation for the tensors. Your way of simplifying complex concepts is truly remarkable and I appreciate the effort you put into making it easy for everyone to understand. Keep up the great work! Reply @williamcaseywells604 11 months ago Here at the end of 2024 absolutely loving this content in an age where vectors and tensors are extraordinarily important and at the very heart of the burgeoning AI revolution. Reply @amelius369 2 years ago excellent explanations. Simple yet in-depth. A great foundation on tensors. Reply @shadowfax8573 3 months ago God bless you sir. This was perfect. For some reason anything that goes from alphabet soup algebra to geometric representation suddenly becomes plainly obvious. Reply @LeoWang24 4 months ago Warning! If you're a computer scientist trying to learn what tensors are, just think of them as multi-dimensional arrays. This video explains tensors in a way useful for physicists and mathematicians but is extra for most cs applications of tensors. 1 Reply @evanlistopad7970 7 months ago WOW! I always knew that playing with blocks and nerf darts would come in handy. I learned all this back in high school and college, but not as cleanly. This makes it easier to explain to those who didn't study engineering and/or physics. Can you do a video on Quaternions? Those still hurt my head to think about. Reply @sw9038 3 months ago (edited) This video is "Hello World" of tensors for AI deep learning 😊 1 Reply @HansHans-yk1mg 5 months ago Thanks for your grate effort and pleasent way of describing this complex subject. Just wonderful :) Reply @nmrp0705 6 months ago wow. you're an incredible teacher. im a physics major abt to be in physics 3 and i so wish i had seen this my first semester. thank you!!!!! Reply @Kuchh_to_Uchiha 1 year ago We need a playlist 1 Reply @nimarezaei4678 5 months ago Thank you this was very helpful Reply @bradfordjeff 4 months ago Never underestimate the power of the pointed stick. Reply @ovidiojosefrancisco4255 9 months ago Very very good! Thanks a lot!! Reply @Дімас7м 2 years ago Great video, but I would like longer explanation in the end Reply @seinundzeiten 1 year ago I love those tools and blocks Reply @thelordbash 9 months ago (edited) Thank you very much for your time :) Reply @RoyBolinggoing 11 months ago This was very interesting for me thanks for the video! Reply @AlbertodeVictoria 2 years ago Thanks for the lecture, master. Reply @SunglassSavant 2 years ago Wow. Thank you so much Dan! Lovely explanation. ❤ Reply @CrueLionJr 2 years ago Amazing explanation. Very direct and to the point. Thank you! Reply @jktrader37 1 year ago Dan this is fantastic ! Thank you ! I love this 3D explanation.. All the best to you Reply @DocMacLovin 11 months ago (edited) You sir are an exceptional teacher. KUDOS Reply @mozengenhocas3595 2 years ago Best explanation. He is the Professor, not a professor... Reply @kurpadmurthy5466 2 years ago Great to know Tensor Basics and Great explanation!! Thank you so much,. Reply @MrLevK 10 months ago Excellent! Thank you! Reply @ValleysOfNeptune2150 1 year ago Thanks for your service ☺️ Reply @Aswin-Prasad 1 year ago Beauty lies in simplicity, and this proves it. Reply @suzukigsxfa9683 2 years ago Absolutely brilliant 👏. Understood it one shot. Thank you sir Reply @crazycala95 10 months ago This video is great, thanks for this knowledge so well explained Reply @travishohenberger7911 1 year ago (edited) I've been working on a video to explain the tensor as it applies to mechanics (static stress) since 2018. I have yet to unify the math and bring it home in my brain. I "get" how it works, but I remain skeptical about the tensor concept...not that it does not work, but rather that I have not seen a clear explanation of what exactly is going on behind the math. What is impressive about Dan's video is how well it ages: he uses no animations, yet manages to explain in very clear terms many aspects of tensors in a practical sense. Reply @tommywilliams1368 1 year ago You are welcome. And many thanks to you. Reply @josealbert7806 2 years ago I would say, thank you for your time, Sir. Reply @venkata.krishnan 2 years ago Dear Sir, I wish our Maths teacher could have taught us this way on this subject, back in the days we did not have so many materials. to get the concept explained like this :-) Reply @chinmaypradhan4399 2 years ago Superbly explained thankyou v.much. Reply @TGP4485 3 months ago Really good video. Reply @sintiayc 1 year ago Thank you for this explanation! ❤ Reply @callme_lyds 1 year ago Thank you so much for this. Reply @jayabratabiswas01 1 year ago Very good explanations 👍👍 Reply @MrNiirmal 9 months ago Sir ji u r too good thanks for explaining in such awesome way Reply @ozeas.carvalho 2 years ago Thank you for your time! Reply @ula7156 1 year ago the best explanation ever!!! Reply @deemo16 2 years ago Thank you for this incredibly clear explanation of vectors and tensors! Anyone interested in the subject of Machine Learning should definitely watch this as tensors are used constantly for data representation. Reply @gurnamankaur_ 6 months ago Thankyou for your time sir. Reply @aecascais 2 years ago Amazing explanation, thank you so much! Reply @saran90tube 2 years ago Please explain the calculus like this simple and clear way. Advance thanks DAN. Reply @benedixtify 2 years ago He’d be a cool teacher to take a class with Reply @haal4056 2 months ago Thank you so much! Reply @vishwasdiwakara 2 years ago Thank you for your time! :) Reply @nikihn 2 years ago Very accurate and understandable, nice vid Reply @Popdad 2 months ago Really great sir Reply @danasugu1767 2 years ago Thank you! Awesome explanation! 💚 Reply @najamuddin9804 1 year ago Thank you sir for one of the best explanation. Reply @ralf7568 2 years ago I was struggling so hard to understand tensors and this explanation really made it so clear. Thank you so much professor Reply @myhobbies5965 2 years ago Excellent explanation. Reply @Ja_Crispyyy 10 months ago OMG THIS WAS AMAZING THANK YOU! Reply @biturboism 2 years ago Pure education with passion for knowledge and love for teaching. No matter how many years of experience one has, it’s always a pleasure to see new ways of presenting these basics. Reply @3dgar7eandro 1 year ago Thanks to you for giving us such a good explanation of such a complex and yet fundamental topic 😁👏👏👌 1 Reply @manelaero7709 1 year ago Thank YOU for your time Sir Reply @binsarm9026 10 months ago Thank you very much sir for such a clear and simple explanation. It proves that no matter how basic or simple the tools are, if you can use them to convey the explanation clearly it is a good tool, there is no need for using computer graphics - those may be necessary for more complex concepts, but i applaud you for using simple items that are relatable to the layperson in explaining a key ingredient in modern knowledge. Reply @xasyo96 1 year ago Amazing explanation! Reply @BhaktShahittoDhar 6 months ago Just, unbelievable!!! Reply @bigredone1030 2 years ago Wow I really stumbled onto a gem here Reply @cleitevieira 2 years ago great analogies! congratulations! Reply @bingbong13 2 years ago (edited) Absolutely genius. For such a complex seeming concept the moment when everything "clicks in" and you know you understand, came after watching the video once. (sometimes it can take hours) You were able to represent rank 2 tensors clearly in about a minute and a half. That is just exceptional. THANK YOU! Reply @LisaRime 1 year ago That is a very very good explanation Reply @thecasualcitizen492 2 years ago Great presentation. Reply @DavidTiptonJr 2 years ago Dan it's so good to find a lecture of yours! I used to work at the coffee shop near your office and I loved our conversations. I hope you're doing well sir and thanks for this information! I've been studying the past few weeks on engineering principles as I work with ventricular assist devices now and the YouTube algorithm recommended your videos to me! 1 Reply 1 reply @binjianxin7830 5 months ago OMG. I’ve been programming Tensorfow until now. Reply @JoaoVictorCavalcanteMiranda 1 year ago Awesome video! Reply @RajeshSharma-bo4oq 1 year ago Wow, Amazing. 1 Reply @krambow1509 8 months ago they should do more guys like this Reply @mirajtohidur3365 9 months ago Thank you very much Sir . Reply @davidben5159 2 years ago Thank you Dan. Great way how you demonstrate by increasing the dimension of the vector that is in the direction of the Y axis which will reduce the Y axis in dimension. Reply @edwardhudson815 2 years ago you had me at area vector Reply @DenisKurovskii 1 year ago Genious video, thanks! Reply @naveenkumarsingh9541 5 months ago Thank you Sir. Reply @theoneandonly947 7 months ago these comments make me so happy 1 Reply @Polynuttery 6 months ago Dan — a wonderful guy ! Reply @enverkilic9226 2 years ago "If you can't explain it simply, you don't understand it well enough", I'm not sure if Einstein actually said that. But to be honest, this video shows that if you know any subject very well, you can explain it very clearly even with some kid's toys. Thank you, Mr. Fleisch, with great admiration and respect. Reply @JoeBob79569 2 years ago I do like this kind of visual learning, but for me this stuff doesn't really sink in until I see several different real-world applications of it. It's like my brain just doesn't buy it until it is absolutely convinced that this stuff can actually be useful. I think this is why a lot of students fail maths, because their brains just refuse to absorb this stuff until they're told how it is relevant. 1 Reply @lonniebrown9063 11 months ago Same for all observers.....powerful! Reply @kuantize 2 months ago This is excellent Reply @glz_br8873 2 years ago Its amazing!!! Thank you Doctor I got the real feeling by now!!!! Reply @aleferibeiro4717 1 year ago First time seeing this, and i Just want to express my gratitude for this vídeo e for the work put to make It!! Thank you so much Reply @sujeshlx 2 years ago Mr. Fleisch , Thank you... Reply @amitmeena5145 2 years ago What an explanation, simply loved the way he explained this topic. Thank you very much, Sir !!! Reply @ratfuk9340 2 years ago This is great, thank you. Reply @HoppityHoppitus 3 months ago I never got by algebra back when I was in school so I didn't understand a whole lot of this but the parts I could follow were interesting and explained really well. Reply @arifahmedbegg2199 6 months ago Truly a blessing Reply @M.A.U2be 1 year ago Thanks for this. Reply @c.mirashi 1 year ago I didn't understand, but I like to pretend and tell myself I understood this great video though, and "thank you for your time." 2 Reply 1 reply @arunakumarisadasivuni7928 1 year ago Superb sir Reply @eduardofukay 2 years ago Great explanation. Reply @hilmiyigit2714 2 months ago Çok güzel bir açıklamaydı, teşekkürler. Reply @michaeldeloatch7461 2 years ago Your whole explanation left me in a state of anxiety, stress, -- in a word: tense! 20th century aviation: "What's our vector, Victor?" 21st century space navigation: "What are Spencer's tensors?" Reply @AndyU96 3 months ago (edited) I like the vectors in coding contexts a lot more than the ones they refer to in mathematics. Vector is an object that can multiple values, each being stored in a different index, but depending on your needs, you can make the indexes have their own sub indexes. That's it fgs. Now use this notation to represent whatever the hell you want. Do you have an object, that is made up of 6 particles, and each particle has a force being exerted on and at various directions? Make a vector of 6 main elements. Subdivide each main element into 3. A subdivision for the magnitute of the x component of the force; another subdivision for the y, another for the z. It's just a damn way of representing something tidily. 1 Reply 1 reply @laurentiubucur9586 1 year ago Thank you for your effort❤ Reply @Bushcamper4Sale 2 years ago Hold on. He said he's only going to use children's blocks then brings in an XZY contraption. I didn't sign up for this. 1 Reply @a_voice_in_the_wilderness 2 years ago (edited) Just realized that I bought the kindle version of his book A Student’s Guide to Vectors and Tensors a few years ago. Had no idea of this person's reputation and knowledge. I found that book very helpful, but (because I was just distracted) never went any further after reading the first three or four chapters. I bought the book purely out of personal interest as a closet student of science, physics etc. Reply @JcPeggy 5 days ago Just great Reply @blind_studios_jp 1 year ago using simple household objects: small arrows 1 Reply 1 reply @suulix 2 years ago Likewise thank you for explaining tensors! Much appreciate the video 😁 Reply @felixsanchezugalde4203 2 years ago I am still a little confused, but from all the investigation I have made to day to understand tensors, I can assure that this brought me closer to understanding. Thank you sir, for your time Reply @baboothewonderspam 2 years ago Outstanding - thank you! Reply @ishangupta1281 2 years ago best. explanation. ever. Reply @ChengziMimikyu 4 months ago That was superrr crazy he made it sooo easyyy Reply @RealLifeTop10s 1 year ago this was amazing!!!!!!!! Thank you so much:) Reply @jhonatanstivenblancomelo968 2 years ago Is amazing and very clear your explanation Reply @AmericanMinutemen 2 months ago Nicely explainedc Reply @Luke-og3eh 1 year ago I really love this. Reply @FATHIMAMEETHAL-r6n 2 years ago excellent explanation... Reply @skjamilahemad4033 2 years ago (edited) I regret that i didnt find him during my school. When i was in school, i used to get confused with these vectors due to lack of visualization. Reply @mrcoolabhishek123 2 years ago Great video sir Reply @havalclaysoldier9688 2 years ago what a wonderful video. best video about the concept of tensors. thank you for your effort very much. Reply @amit_38ycx 2 months ago Thank you so much sir Reply @arasgoshayeshi9156 2 years ago Such a brilliant video thanks very much 👏👏🙏🙏 Reply @rishu4225 2 years ago Thanks so much for your hardwork Reply @neeth35 2 years ago Such a good explaination Reply @andredeleon6194 2 years ago Fantastic explanation on tensors. I struggled visualizing and understanding 2d vectors studying mechanical engineering years ago, but this video broke is down so easily! Simple to understand explanations like this help reinvigorate my passion for learning new subjects! Reply @Dracopol 11 months ago I first heard of tensors as a boy. Alfred Bester wrote THE DEMOLISHED MAN, a novel about a society full of psychic individuals and a man who wants to murder another man despite all the mind-readers present. Part of his plan is to cloud his thoughts with a repetitive jingle which is "Tenser, said the tensor. Tension, dissension, apprehension have begun!" Reply @deepakvenkatesh5166 2 years ago This is great! Thanks! Reply @wymow716 2 years ago Thank you so much for this video, sir Reply @Silks 11 months ago I think it might help to hear some practical applications of tensors Reply @larrydugger2971 1 year ago Thank you kind sir. 😊 Reply @Mokar-ali 2 years ago Thank you for your time Reply @SarahMMorsy 3 months ago wow!!! THANK YOU!! Reply @twisted4872 2 years ago Amazing explanation Reply @n-da-bunka2650 2 years ago Now we just need to figure out a tensor for time and space Reply @RickySupriyadi 11 months ago oh my... i remembered my high-school Reply @probaho3671 1 year ago Beautiful sir... thank you very much Reply @JesusIsMySaviorILoveJesus 2 years ago I’m only in precalc but even I was able to understand this well. This is was well explained, amazing job. Reply @emanuellandeholm5657 2 years ago This is such a good tutorial on tensors! I used to believe that tensors were just generalizations of matrices, but it turns out that tensors generalize vectors. Reply @nathan87 2 years ago Never in a million years did whoever made those blocks think they would one day be used to explain graduate-level mathematics. Reply @RealJesseAdam 2 years ago this is vsauce2’s dad 1 Reply @rustamstolkin4083 11 months ago (edited) I would have liked to see a simple 2D matrix as a stepping stone between 1D vector and the Tensor. I felt the vector introduction was a bit too long and simplistic, then the jump to the 2D and 3D Tensors, each with multiple components, was too fast for me to maintain/keep up a clear understanding at the deep/simple intuitive level. E.g. why is a 3 by 3 inertia tensor called a "tensor" and not simply a "matrix"? I would like to see some clear explanations of these things - but am left still feeling very hazy despite such math being important to my own research area. 1 Reply @rmbf57 2 years ago The best visual explanation I've ever seen!!! Thank you, sir! I'd wish have watched this video during I was at school. Now I study energy engineering but this explanation still being satisfying for me. Reply @ReyhanehFeiz 2 years ago it was so useful thank you Reply @markkennedy9767 2 years ago (edited) Great video. The fact that there are so many comments here saying that their professors could not explain this is very worrying about the state of higher education. These commenters aren't stupid (they get the essential idea of a tensor after a ten minute video). Something they were unable to get from years of "teaching" by experts in their field. It begs the question what do these experts actually understand themselves. After all, there's some truth behind the idea of "if you can't explain something simply, you don't have a proper understanding of something". It's not wrong to conclude that there are so many experts in university that don't have a good, full understanding of these concepts. They have understandings, definitely. Enough to get high marks in exams, go on to grad school, get PhDs and become tenured professors. But it's a shitty working (typically symbol-pushing) understanding and certainly not the type of understanding that Prof. Fleisch has. What I call a proper understanding. Reply @ArionXeno 2 years ago Excellent, thanks. Reply @MichaelChin1994 2 years ago I appreciate your video and your passion. Your enthusiasm is contagious! There were some things I'm still confused about, though. In the last section, what was the third component of the tensor supposed to represent? Also, I still didn't understand why tensors are important? It sounds like just another way to express a vector. Is it just condensed? Reply @JohnRambo-e6o 3 months ago Thanks master! Reply @mathmetics12345 2 years ago Sir, thank YOU for your time! I studied these tensors in materials back in uni and only YEARS on do I understand what they mean! Truly a wonderful educational experience 😊 Reply @stardeastroyer 2 years ago Great video! Reply @MananaMan 1 year ago My interpretation is that you can almost think of it like putting parenthesis around numbers and distinguish what is included based on what dimension you’re dealing with. 1st (3,4), 2nd ((3,4),(4,5)), and 3rd dimension (((3,4),(4,5)),((1,2),(2,3)),((5,6),(6,7))). Idk if that’s correct though. Also I’m wondering if calling the component a compliment (like in statistics) is correct or not. This video is so invaluable I would have never imagined myself liking math. Reply @CharanTheAIguy 2 years ago Guruji, Danyavadh, Reply @Aristothink 2 years ago very good and deep explanation. There are so many videos trying to simplify the concept but they end up making it even more complicate. Your video is very clear.... Thank you very much for such a class !! 🏆🏆🏆🏆🏆 Reply @pretzelsareyumy 4 months ago Peace, Thank You Reply @arunattnj 1 year ago Jaw drop at the end. Pure love for curiosity. Reply @elieelkhouryfarhat7686 2 years ago Mr you are a genius 👏👏👏 Reply @damiansenpai9501 2 years ago Nice video Mr. Fleisch, this is my first time studying the topic of tensors, i am studying chemistry engineering and in this moment i am studying for transport phenomenon, it was quite intersting, and it was a little hard for me because i dont speak english, but i did my best to understand the video, i really appreciate the time you took to do the video, thank you so much. Reply @zamansmail 5 months ago So Useful. I wanted to give more than 1 like. Reply @ExcitedPunch 2 years ago I loved it when he unexpectedly got out the parentheses. LOVED it. Reply 1 reply @markhonea2461 2 years ago I am learning more and more on youtube. I learned very many things of much importance to myself and my research on Google, 10 to 15 years age but Google seems to have sold out to advertisers and now is nearly useless without much struggle. Did I mention I'm old, in years? Oh crap gotta start this video over I've been talking WAY TOO MUCH!! 😂 1 Reply @kaylabunga1567 10 months ago No, Mr. Fleisch. Thank you for YOUR time. 1 Reply @silaskelly604 2 years ago (edited) It is a very good presentation to explain basic tensors and that a scaler and a vector are subsets of a tensor. I hope you will continue and create another presentation of tensors with 4 and 5 dimensions. After all this time, I still have trouble visualizing space-time warping and curvature. It's such an interesting rabbit hole that deserves exploring down further. Reply @ergadas 7 months ago Thank you, I do not have other words. ❤ Reply @turonb 5 months ago Best explanation Reply @rajisingh5710 2 years ago Amazing Amazing explaination Reply @peters972 2 years ago (edited) I’m glad I know now and thank you Reply @siddhantjain243 2 years ago I got lost in 2nd rank tensor 1 Reply @suga2420 1 month ago thank you! Reply @DANTHETUBEMAN 2 months ago I generally new about the 3-D space position, but not the forces on the position. Reply @CdevAtReco 2 years ago This reminds me of arrays in programming. Guess they're connected concepts. Reply @camilochaparro8781 2 years ago Nice video! Glad to see that someone did not stick in the annoying and quasi-tautologic definition that "a tensor is an object that transforms as a tensor". Reply @Johan-rm6ec 2 years ago I love this man!!! Reply @lolaa2200 2 years ago We should pay you to teach maths "teachers" how to actually teach Maths ;c) That is a masterpiece. Reply @southparklion 9 months ago If I had this video when I was in graduate school, I might be a PhD now. Reply @debabratasahoo98 1 month ago What a masterpiece Reply @thisrandomdude_ 2 years ago Fantastic explanation!! I''ll need to study the specificities a bit to understand it more, but this serves as a crystal-clear introduction to the topic, even 11 years after it was released. Reply @davidjones5319 11 months ago Excellent! Reply @thomastse6228 4 months ago My first time... For some reason YouTube knew I am interested Reply @mahrezaitm.5162 2 years ago Thanks Daniel ! Reply @ofthechase6962 4 months ago THank you sir Reply @Raven_4567 2 years ago наконец-то, человек который говорит не сложными словами а показывает. Reply @Palau_Legend 10 months ago Wow. Thank you. Reply @zylascope 2 years ago Thanks. I'm getting there :) Reply @markgreen2170 2 years ago that was good! thank you! Reply @anonymoususer4356 1 year ago Excellent! Reply @azlinafiroz667 2 years ago A masterpiece 👌👌 I have never witnessed such good explanation of any concept previously 👌👌 I must salute you for delivering concepts in such an effective manner Reply @gokulchandran5586 2 years ago Thank you very much. Reply @halgorithmist 8 months ago Thank you for your service o7 Reply @kuhumbuwa 2 years ago Superb🎉 Reply @rulojuka 10 months ago Bro explains tensors in 12 minutes and calmly takes 8 minutes reviewing linear algebra basics. Amazing! Reply @Atomanti400 6 months ago Thank you! Reply @MentatTrain 1 year ago This is how you should teach something ! Reply @uno_king 3 months ago I took an entire semester on vectors and tensors in college. Only thing I learned was I wasn't going any further into math than Calc 3 (which was the semester before). Reply @a-levelking8610 1 year ago Very good video Reply @Willientus 1 year ago Am I the only one who heard a "Oh Yeah!" around 0:42 . Great explanation too thanks for the lesson. Reply @jee2026-w8v 2 years ago great explaination Reply @edwardperry5041 6 months ago Well done. Also +1 for the "point-ed stick" cf. Monty Python. Reply @yvessoke8558 1 year ago Thank you sir. Reply @TheMemesofDestruction 6 months ago (edited) Thank you! Reply @raagulkhanna2967 11 months ago thank you so much sir Reply @MDMUKTERALI-b6j 9 months ago Crazy...❤Genius in It's simplicity ❤ Reply @rauldelgado4372 2 years ago Sir, this videos is simply great. And if you don’t mind, I will use it as inspiration for my high school Math lessons. Thanks for this amazing jewel of education 🎉 Reply @MichałPiwowarczyk-e2p 1 year ago SUPER, Thanks Reply @sohamsavarkar763 2 years ago Amazing video Reply @rekhtabyalihassan1505 1 year ago very very very nice!!!❤ Reply @arunms8696 1 year ago Thank you sir ❤ you're amazing ❣️ Reply @onicarpeso 2 years ago 11 years later... after ChatGPT and AI... I am here to start with the basics. Reply @bobbybooshay8641 2 years ago (edited) They're those things kids used to have taken out back in the sixties and seventies. Reply @DecidersCreation 4 months ago thank you sir Reply @NelsonboadaMovil 1 year ago Maravilloso, el que conoce realmente de un tema normalmente logra transmitir el conocimiento Reply @luuksemmekrot4509 1 year ago Thank you very much Reply @Barnaclebeard 2 years ago I've never heard someone put the emphasis on the first syllable of "component". It's interesting. Reply @MT.632 2 years ago Worth watching ❤ Reply @ferencandras2118 2 years ago Thank you so much. Reply @amitabhranjan9668 1 year ago Thank you sir. Reply @iLikePlanes16 8 months ago Thank you! Reply @speedingAtI94 2 years ago Commercialize this, YouTube! Reply @sebulba4864 1 year ago 0:28 Today you'll learn how to defend yourself against a Tensor that attacks you with a pointed stick. 1 Reply @ary_swam 1 year ago Those who came from Daniel Bourke tensor flow with Deep Learning video ---> ✨🖐️ 1 Reply @aryantyagi3288 7 months ago I have always know and use vectors in my work and also proofs but never did i understand it like this. Reply @ashisghosh9349 2 years ago THANK YOU SO MUCH SIR Reply @huskypup3489 1 year ago It’s not clear why the combination of components and basis vectors would transform in such a way that all observers agree. 1 Reply @Johnathonaaron 2 years ago I have no idea what you are saying but I like how your saying it. This was a great use of props. I'm at about an 8th grade math level but I think I can see how these tensors can be used to model all kinds of complex interactions. I have no idea but it seems like you can use these to model stuff like particle interactions in a fission reactor to current in the ocean. Reply @eukaryote9332 2 months ago Too good 👍 Reply @arnab6408 1 year ago 'One what?'....teachers forever preempting students questions Reply @bashirrather1562 2 years ago Thank you sir. Reply @imnbmusic 6 months ago This is gold Reply @Cheetah_727-l5v 9 months ago Thanks professor Reply @RM-yw6xe 2 years ago ... a topic my family and I can never talk about. Reply @johnypayeras 8 months ago Thanks Proffesor !!!!! Reply @mohamedalkaabi1231 2 years ago Thank you sir. Reply @FrankWolf74 1 year ago Thank you! Reply @Ab.Stat. 2 years ago Outstanding! Reply @DiegoRamirez-vf1yt 6 months ago Absolute cinema Reply @ErnieStephenson 2 years ago This is great. Reply @just_a_viewer5 9 months ago Thank you sir Reply @Sleeperknot 2 years ago (edited) In a parallel universe, Dr. Fleisch went on to show a 4-dimensional tensor in a 4-dimensional space in TesserTube, their video-sharing platform. Reply @michaelstewart7871 1 month ago Please produce a follow on video showing how to apply tensors by solving a mathematical problem. I sort of grasp the idea, but not fully. I need to see a practical application. Reply @przemysaw6539 10 days ago Very good explanation, but there seems to be one arrow missing before the last block. Specifically, at the Ayxx position 🙂 Reply @stardust-r8z 6 months ago A tensor is a coordinate-independent quantity. Equations of physics are expressed in tensor form like Newton's second law (which forces forces to be conservative i.e derivatives of potentials), the Einstein field equations, the Lorentz force et cetera. Reply @yahyasheikhnejad 1 year ago It was a very nice representation of vector and tensors. However, I noticed that 95% of time was spent for the simplest part and 5% for the hardest part of this concept. I do believe that the sentence started at 11:30 and end at 12:05 needs an explanation by a new video. To be honest, I watched this video just to understand the last sentence and have a deeper perception on the most important feature of tensor and I got disappointed. If there is any video about that, please help. 1 Reply @justinf.5688 8 months ago As calming the voice of Professor Fleisch has, I feel like I did not really come out of this video really understanding what a tensor is, it's a shame he did not expand on the transformation rules on the tensor aside from a brief remark at the end of the video, since it seems that is the essence of tensors. Then again, for the lack of fancy animations it's quite a nice video! Reply @expensivetechnology9963 1 year ago #DanFleisch you are a gifted instructor! I wish you would have continued your instruction a little longer. I remember what Einstein said about reference frames related to an elevator in his thought experiment. But I need more help to understand how tensors related to reference frames. Reply @flixerstudios1862 1 year ago They are multilinear maps over vectors spaces Reply @nonokodog622 11 months ago Nice English furniture and fun refresher. I suppose the compact notation Ae^ia+b is also a tensor yes ? Reply @VikrantSingh-se2zb 1 year ago För the first time in my life I understood the deep technical concept of vector tensor imaging transformation techniques from pixel, to voxel levels scaled resolutions referencing frame projected onto observational quantum mechanics guided spherical arrays of hypercube looped plane tracing source, distance and targeted timeline weighted frequency domain. Thanks you very much for illuminating me on hidden facts of the universal multidimensional naked singularity of truth which penetrates mythical mindset body Integrative spiritual anatomy. Reply @harvesterharvester 1 year ago Wish all my teachers were as smart ! Reply @i2c_jason 2 years ago I think he wrote my Electromagnetics book... anyway thank you for this clear explanation with blocks. I learn at a 1st grade level, but once it's in my brain I retain it. Reply @sebastiansleek5456 1 year ago God bless you 1 Reply @pyramidiots 11 months ago have a feeling this vids about to get a L O T more popular Reply @cadmean-reader 3 months ago Quality content Reply @DanWills 1 year ago Fantastic explanation, thanks so much! I feel like I understand tensors a lot more now! Seriously appreciated! I reckon I might be the perfect audience for this video because I use vectors a lot (job in VFX) but I have not ever used tensors! I think certain types of VFX simulation solvers might use tensors 'under-the-hood', but I haven't gone deep enough on that myself to really know. Our Machine-Learning department at work certainly does use tensors a lot! (perhaps kinda indirectly?) But I'm still wondering what I could use tensors for in a simple everyday VFX/shading/geometry-processing or maybe simulation use-case. Here are some examples of some ways I've used vectors and vector operations: - Dot Product: Find how much 2 vectors point in the same direction like find the side of an object pointing towards another position. Classic 'Lambertian' diffuse shading (dot product of surface-normal and light direction). - Cross Product: Get the orthogonal vector for 2 other (normalized) vectors, lots of harder-to-describe use-cases, but for example getting a vector that 'goes around' instead of 'towards/away' from something. Or getting the third axis when u only have 2, or indeed correcting 2 vectors that are not orthogonal to give the closest orthogonal result (the good old "double-cross"!) - Vector Projection: Finding the Z-depth of a point in the scene given the camera view direction, or indeed more generally how far along any other vector we are. I loved your shadow analogy! That's pretty-much what I imagine when thinking about projection myself too! - Separation of a vector into length and direction components via the 'length' and 'normalize' operations: Allows one to do things purely to either direction or length and then reassemble the result by simply multiplying back together! - so useful for radial-spatial-warping around a point, or mixing vectors with separate amounts for amplitude and direction, etc. Anyway.. I went-on too long again, youtube probably isn't the right place for this kind of talk but I'd love to hear if anything springs to mind that I could try myself that might be a good illustration of how one could use tensors to do something useful that is hopefully similarly easy to describe? Reply @jacobandrews2663 2 months ago Thank you very much! I understood, in summary, that as indivudual sets of, let's say, sub-vectors transform, their categorization, keeps track of individual objects. yeah? Reply @imkarthikbhasi 11 months ago Why does youtube always recommend this to me after the exams!!!!😓 Reply @grandmasters_educational5353 6 months ago Oh professor in India we learn it as onemark twomark questions. Reply @yeonhyungjun674 2 years ago It was superb explanation! I am going to learn tensors for understanding general relativity, can't wait to read your book! Reply @doubop8021 2 years ago nice video, it's what i call the real approach of the physics..by itself (using items shadows…) Reply @reaganlopezmusic 2 years ago wow.. Thank you so much.. Reply @Calamarydeniro 2 years ago Muy, muy bien. Thank you, it's a nice explanation Reply @LadyVitality 2 years ago EXCELLENT!!!!!!!!!!!! Reply @RD_Joe 2 years ago This man must be protected at all costs! Reply @FireFly969 1 year ago Thank you so much Reply @Spiegelradtransformation 1 year ago Well Done.👍 Reply @hellopsp180 2 years ago That was pretty cool Reply @jee2026-w8v 2 years ago killer visualisation Reply @jamesbirmingham3110 2 years ago Thank you so much Reply @pankajkumarpandey6658 5 months ago Excellent Reply @faithrunner1813 2 months ago Спасибо, сэр! Reply @cansucorbac1514 1 year ago 🥹💜💜thank you a lot! Reply @jordyward1952 4 months ago Incredible Reply @nicolasaugustokozameh4810 1 year ago Thank you! Reply @quadrupleheart 2 years ago Don't know why I'm here but I loved it Reply @mahadevs7168 2 years ago Thank you sr❤ Reply @trailcarver3018 11 months ago outstanding Reply @jarleydg 2 years ago Thank you!. Reply @ninjaengine1471 2 years ago the facted that even a 9 grader could have understod the basics of a tensor in this video is icredidle Reply @indroneelroy5043 1 year ago Salute Sir. Reply @MAHADEVS-l5m 1 year ago Thank you sir❤ Reply @JacobP81 2 years ago 6:57 Yes that's just the basics of the coordinate system used to digitally encode a vector graphic. I already know this. You explained it well though. This system is also the underlying system of CGI graphics and animation. The value can be stored in an xyz array. This system is probably also used in video game design. It is a very basic foundational principal or representing shapes. Reply @nik3932 2 years ago infact thank you very much.... Reply @armaanmalhotra9042 2 years ago 🔥🔥 1 Reply @3xarch 2 years ago i get how the level 2 tensor represents all directions and all possible forces acting in those directions, and my next question seems self evident after writing that: what could the extra level of components in level 3 possibly represent? seemed like we had it covered in level 2 haha Reply @clavierwintergreen5574 1 year ago Hope you meet you in person so that I can shake your hand! Reply @mohammedismail6872 2 years ago little did he know that this will be the build block of a revolution (ML) Reply @rodrigorsfo 2 years ago I watched it a first time, in the last part I went: WTF?! Watched a second time on specific parts to clarify the terms and definitions... then rewatched the conclusion and went: OMG!!! Amazing video :-) Thank you professor. Reply @Massenko 2 years ago Thank you sir Reply @SportsIncorporated 2 years ago Was I the only one waiting for LEGO blocks? Reply @armintabesh6825 2 years ago I hope he found the unit vector under the table, on the carpet. Reply @HorrorInsides-dm8fc 1 year ago (edited) Thank you very much Dan. This is probably the best explanation in the public space for Tensors. Had a quick follow-on questions when you were representing the rank-2 tensor in the 3-d space. Should we envision each of the A components i.e. Axx, Axy .... to be a multi-part numerical value like (3,2), (4.5,7.6)? Or is it just a single value. And do the basis vectors have to be orthogonal to each other? I am trying to firm up my intuition behind tensors. Many thanks. Reply @alexsapozhkov4665 2 years ago Correct me if I'm wrong but there seems to be some small flaw in this video: on the minute 10, when they demonstrate rank 3 tensor. As far as I understood it, there should be 3 sticks in each of the groups. However, one of the groups seems to only have two sticks Reply @salehelgaberty 2 years ago Dr. Dan, Thanks for your simply explanation, yet i had to watch it 5+ times to digest it to make sure i clearly understand it .. i guess this is the back bone of AI (: Reply @wideeyedraven15 2 years ago That is how you teach. Bravo. Now, if we could just do something about how you pronounce the word ‘components’…😂, but seriously, wonderfully done. Reply @zapthathattrick 2 years ago I never understood it until now. Reply @billknight7442 11 months ago I went to buy my son a foam dart gun for Xmas and they were out of extra darts, now I know who bought all of them! Reply @jamestait324 1 year ago I'd always thought of Spacetime as being a scalar. Why? Because space is described in terms of distance and time is described in terms of duration. To me, distance and (perhaps) time have magnitude only... and would seem to be scalar properties. But if an area can be thought of as a Vector (as mentioned early in the video) then could you think of Spacetime as being comprised of multiple Vectors? This is especially so when you consider the time component of Spacetime. Since Time seems to have a direction. Now comes another idea which might be jumping ahead a bit. The power of Tensors is that there's a common reference frame for all observers. This reminds me of how speed of Light (a vector) moving through Spacetime (possibly being thought of as a Tensor field?) is the same to all observers no matter what their reference frame. Reply @arpanmukherjee4625 2 years ago Thank you so much for explaining this concept of tensors so easily. For my purposes in programming and math, tensors are just n-dimensional matrices anyway 😂 but I didn't know the physical implications of that (for vector we have all read, but tensors I never visualized). Reply @RobertKnowsAll 2 months ago Learning! Reply @jacoblingwall6767 2 years ago I'd take your classes :D Reply @rajeshkumardolai 2 years ago Excellent Reply @EdwardElric-uf3rr 2 years ago I wish i saw this in college Reply @ShailendraKumarGupta-e3r 6 months ago he killed it Reply @joxa6119 2 years ago (edited) Just for the 2nd rank tensor, it supposed to be represented as square on a paper instead of a pile of bricks, as it is in 2 dimensional compare to 3rd rank. And need a warning that we cannot imagine in our head the 4th rank tensor. Reply @404nnotfoundd 9 months ago Thanks <3 Reply @better_dead_than_red 2 years ago Love his head. Reply @nikogoat14563 2 years ago Too helpful Reply @amjedali82 2 years ago wonderful Reply @missinglink2416 2 years ago (edited) fuck i really thought im an idiot after not understanding the topic and concepts in the first to 5th try.. the 6th try finally hit me!!!!!😂😂😂😂😂 i can continue with machine learning..hahahaha Reply @andrewking8616 6 months ago Legendary goat Reply @k4r4m310. 1 year ago hand-pink-waving Reply @SubEthaEngineer 2 years ago beautiful Reply @nullaxflexi4378 9 months ago Legend dude Reply @TheJimtanker 2 years ago People who can make complex ideas very simple are a treasure. THESE people should be paid like professional football or baseball players. Why do we pay people so much money to play with their balls? Reply @selforganisation 2 years ago Great video. I have a question: what quantity could the rank 3 tensor represent? Reply @NT-og5sq 2 years ago When he takes out 2 parentheses for real, i couldn't help to laugh. So cute !!! Reply @Govstuff137 1 year ago I'm impressed. Now I need to figure out how to incorporate level 3 tensor into an XYZ coordinate system driven by time as a separate component of the level 3 tensor. Or has that been done already? Reply @josephshaff5194 1 year ago Thanks ! Reply @fletchergull4825 2 years ago You are awesome Reply @terenzo50 2 years ago Tensors were small inexpensive desk lamps we could buy in many slightly different styles and colors, but always with one pinned bulb at the end of a telescoping arm. Late 1950s to early 1960s at an import store called the Akron where all the diverse goods were from somewhere across the Pacific. Any other use of the word I don't know anything about. Reply @Ihsan_khan00 2 years ago Nice thanks Reply @saschaschneider9157 4 months ago I had a vague idea what a vector is, but I didn't knew it could be represented as a triplet of variables. This whole thing seems to me like arrays in programming, where sometimes we have to deal with 2- or 3-dimensional arrays. Not sure if this applys here. Reply @valeriarivera1982 1 year ago AMAZING Reply @gerardopc1 2 years ago For those of you who want to understand tensors so badly, I highly highly recommend this book for beginners: "Vectors and tensors by example" by author Richard E. Haskell (2015). You won't be disappointed! 1 Reply @salimallami5790 2 years ago Thank you from algeria Reply @OctavioMoya-od5jr 2 years ago This guy broke the education server Reply @markhonea2461 2 years ago Haha some of this runs through my head everything I calculate distance when lopping off corners when traveling. In a very raw and uncalculated vector sort of way. Reply @abhimat 2 years ago Thank you Reply @sammarah7736 1 year ago I bet you didn't guess that your baby sibling's missing number cubes were being played with by your uncle in a dark room. Reply @Linguaexpress 1 year ago Very cool Reply @beyondbirthday4212 1 year ago thank you Reply @saiprem5380 1 year ago amazing Reply @jirosuzuki2317 1 year ago (edited) @dfleisch Thank you for the lesson. You gave a physical interpretation of the Rank 2 tensor (forces acting along an area face), what is the physical interpretation of the Rank 3 tensor (cube) - two independent forces acting on the same face/area? Reply @BobHeartsYou 6 months ago Well you just unlocked the universe for me. So it looks like these 3 and 4 tensors are used almost to give agency or state to particles in a system, giving you a transform to apply for every tensor in the field? Reply @edbail4399 1 year ago Nice group Reply @ahmedqureshi4831 1 year ago No! Thank you for your time. Reply @sambacarlson 2 years ago If all my teachers in college explained everything like this, I will no doubt be the Albert Einstein of our time, if not better.😁 Thank you sir for the very clear explanation Reply @Federico-1 2 years ago Nothing what’s a tensor with you? 1 Reply @labeedkhalid 2 years ago amazing Reply @Bootmahoy88 2 years ago He took a potentially befuddling subject to non-mathematicians and communicated it in a very simple so that anyone can understand it. He really understands the subject. Reply @lowlightevangelist9431 2 years ago When you put parentheses around the blocks the light came on. Thanks. Reply @stevebaryakovgindi 2 years ago thanks! Reply @vikramjirgale8855 2 years ago Very beautifully explained. I agree with the comment by @toddpnewton - Thank you for your time sir. Reply @WideCuriosity 2 years ago The shadow ain't that clear, and one didn't need darkened rooms & a light to show the blatantly obvious anyway. I think it just complicated it. 1 Reply @mcasualjacques 2 years ago well 4 years ago i was here, now i'm about to learn just enough tensorflow to make my locomotion control for my humanoid ( meaning not a robot with cafeteria-tray-sized feet ) robotte Reply @aaioumslm3766 1 year ago Thanks 1 Reply @syfy-p6y 11 months ago great❤ Reply @youruniquehandle2 2 years ago This is a great explanation but all I can hear is Kevin from the office. Reply @outofpie7688 2 months ago Wow this is what a genius is. Reply @hqs9585 1 year ago Brilliant Reply @citricdemon 1 year ago good question Reply @ZbigniewLoboda 1 month ago ❤❤❤❤❤ Reply @ManuelLopez-zq9up 2 years ago I'm on minute 5. I found he took the "let's project the vector into X and Y axis" quite literally. :-D ut hey, here you can get 100% why using "to project" to do that. I have not yet arrived to the matrix and tensor and it is interesting already. Reply @brandonmarquette7476 2 years ago Now do Spinors and Twistors! Reply