I never intuitively understood Tensors...until now!

I never intuitively understood Tensors...until now! FloatHeadPhysics 605K subscribers Subscribe 44K Share Ask Save 1,089,769 views May 16, 2025 3 products FloatHeadPhysics tagged products below. Learn more I don't give a flux $18.99 floatheadphysics.com/products/i-dont-give-a-flux?variant=06598303-4579-4c95-b2a0-94f71ec96562 Don't be a Jerk! (Light) $18.99 floatheadphysics.com/products/dont-be-a-jerk-light?variant=073b5964-54a6-4f30-b39f-4d4b1fbd3912 Paranormal Distribution (Light) $18.99 floatheadphysics.com/products/paranormal-distribution-light?variant=187221c4-f99b-49fa-9647-4363d913bc6e To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/FloatHeadPhysics . You’ll also get 20% off an annual premium subscription. I don't give a flux T-shirt https://floatheadphysics.com/products... What exactly is a tensor? Chapters: 00:00 What exactly are Tensors? 01:23 Analysing conductivity in anisotropic crystals 03:31 Is conductivity a vector? (hint: nope) 05:00 The key idea to understand Tensors 07:07 Rotating the co-ordinate axes (climax) 10:48 Why are Tensors written in matrix form 11:50 Conductivity is a rank-2 Tensor 14:14 Rank-2 Tensors in Engineering & Astronomy 17:48 Rank-3 & Rank 4 Tensors in material science 20:29 The most intuitive definition of Tensors This video is sponsored by Brilliant.org Chapters View all Transcript Follow along using the transcript. Show transcript FloatHeadPhysics 605K subscribers Videos About 2,217 Comments rongmaw lin Add a comment... Pinned by @Mahesh_Shenoy @Mahesh_Shenoy 7 months ago To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/FloatHeadPhysics . You’ll also get 20% off an annual premium subscription. 117 Reply FloatHeadPhysics · 25 replies @ishaan863 7 months ago "we're gonna PRETEND we dont know anything about tensors" you pretend brother im method acting 5.6K Reply 35 replies @absolutedesi5899 7 months ago The part where you ‘got lucky’ can be interpreted as you selecting the eigenvectors of the transformation as your basis, essentially you’re diagonalizing the matrix, hence only the diagonal elements remain. 🤯 1.5K Reply 38 replies @ThomasKuncewicz 6 months ago I love how you say 'to which Feynman says', keeping his spirit alive in this video inspired by his lecture. Your enthusiasm is so sincere and makes your content even more fun to watch. Thanks for making this 1.1K Reply 12 replies @Chipchap-xu6pk 5 months ago I'm getting very jealous about the amount of one to one tuition that Mahesh is getting from Feynman 543 Reply 4 replies @MH-dn3jz 5 months ago Dude this is SICK and I love your enthusiasm. I asked everyone from high school through grad school what a tensor was and I got "You don't want to know." This is SUPER helpful. 187 Reply @joserobles6679 7 months ago I have watched a lot of videos of people explaining tensors. NONE of them as clear and intuitive as this one. Thank you so much! 543 Reply 3 replies @Jetstreamer0 7 months ago I'm 100% interested in more on this! In fact I'm sure all the engineering community could benefit from increased intuitive understanding of tensors! 763 Reply 11 replies @peterhall6656 7 months ago (edited) 50 years ago I partially reconstructed how Einstein learnt tensor calculus using the textbooks and papers of the time. Everything was highly analytical with very little visual content unlike today. I invite viewers to open up Levi-Civita's textbook on tensor calculus from the early 1920s to get a feel for the vibe from those days. By the way the teeshirt is fantastic - I bought one for me and one for my son in law. 380 Reply FloatHeadPhysics · 14 replies @rutwik_113 2 months ago Scaler: just a number signifying magnitude Vector: magnitude in a particular direction 2nd Order Tensor: magnitude in a particular direction at a specific point of application 24 Reply 1 reply @vewmet 3 months ago Bringing the viewer directly into the discussion and also sharing that you don't have the mental capacity to visualise these big tensors is actually very valuable. This is because I know a lot of students who have very strong visuals and they try so hard into visualising everything before telling themselves they understand it. but sometimes what to not think too hard, and move on without wasting time is important too for real progress. 37 Reply @dyutimanmondal8582 7 months ago vote for intuitive explanation of einstein's field equations.................... 101 Reply 4 replies @ShlokParab 6 months ago 0:27 "I don't give a flux!" 72 Reply @perrymaskell3508 7 months ago I'm a Mechanical Engineer. I learnt the stress tensor (and the torsional one too) way back when. So I am used to the concept of things being different in different directions. But I never thought of it like this. Bringing things together to make practical sense. Well done. 84 Reply 2 replies @johnreid4830 5 months ago The idea of intuition first, mathematics detail afterwards is a very powerful one. Very well done. 10 Reply @SteveMould 1 month ago This is the second of your videos I've stumbled upon. Really great way to learn! Thank you! 10 Reply FloatHeadPhysics · 2 replies @LedZeppelinPage 7 months ago This is the most intuitive explanation of a tensor that I have ever seen. As an engineer, I just approximated the definition of a tensor to be something that transforms like a tensor... Thank you for your amazing contribution to education! 197 Reply 5 replies @doge_69 7 months ago You and 3blue1brown are now my favorite channels on youtube 148 Reply 2 replies @bharath__100 7 months ago Student: sir ...What is a Tensor? Teacher: Anything that transforms like a tensor , is called Tensor . Student: well then...What things transform like a tensor? Teacher: well ....TENSOR 269 Reply 7 replies @andremoire 2 months ago I’m working on a real time physics engine, and in order to do this, inertia needs to be represented as a tensor. I didn’t really get why because back in high school, we only viewed inertia as a scalar, and I haven’t done any physics since. I got the whole direction thing, but I didn’t understand why I would need a whole 3x3 to describe it. This video was a good starting point for me to take a closer look at what a tensor really is instead of just thinking “well that’s how it is” 6 Reply @brendonbalascan6814 1 month ago I have a degree in physics, and I’m putting it hard at work by smiling and saying “haha yeah I know what that’s about” at 5 am 10 Reply @glenc5185 6 months ago Pretend I don't know anything about tensors ... I don't need to pretend.. 40 Reply 1 reply @dr_ned_flanders 7 months ago I finally understand this intuitive explanation of tensors, so now explain the difference between covariant and contravariant tensors and the transformations between tensors. 97 Reply FloatHeadPhysics · 13 replies @fahadguru 7 months ago 1:00 No need to pretend 😂 I dont know anything about TENSORS 65 Reply 2 replies @HareshVenkataramananG 6 months ago At this point, Feynman lectures have the answers for everything now. 17 Reply @JoePhilli-DIY 5 months ago Came for understanding what an AI tensor is, stayed for the physics 40 Reply 5 replies @johnclark8359 7 months ago You have an uncanny ability to be able to explain complex things clearly, this is one of your very best videos and you've made a lot of great videos. I hope you make more like this because I'm interested in general relativity. 65 Reply @ScrappyDoodlez 7 months ago Your passion makes me so happy 15 Reply @janplys2954 7 months ago (edited) I've never seen anyone as excited as this guy talking about tensors. 30 Reply 2 replies @antovfukov9005 5 months ago You missed an opportunity, instead of saying "mathematicians abstract the hell out of it," you could have said, "mathematicians abstract to the nth degree." 😂 Yes, I am a dad. 48 Reply @user-dialectic-scietist1 3 months ago 2:10 It is like Newtonian mechanics and Lagrangian mechanics. But if someone gives an entire lecture without beginning with a definition, this means that even he has no answer to the question. 5 Reply @aeolyria 7 months ago Mahesh, you are definitely one of the GREATEST teachers of physics I have ever seen. I think I'm finally figuring out what a tensor is thanks to this amazing video! I would love to see more stuff about tensors from you! 50 Reply 1 reply @fahmidafarjana7366 7 months ago Sir please make a video about hybridization of otbitals 22 Reply 1 reply @guruprasadr6743 6 months ago Possibly the best video when it comes to explaining a Tensor. 28 Reply @Daek3sh 5 months ago I think this is the best explanation of tensors I've ever seen! Thanks FloatHeadPhysics (and Feynman!) 4 Reply @exzonom99 1 month ago I am studying masters in mechanical engineering and every subject that i am studying revolves around tensors in one way or the other. No one, including my professors, were able to explain what exactly do tensors mean. Thanks to you, now everything makes sense 1 Reply @anrwlias 7 months ago This is my absolute favorite science channel. The way you explain things is great. You don't dumb anything down, but your explanations aren't opaque, either. 51 Reply @NAMITADALAL-pz9wj 7 months ago (edited) 5:52 I was thinking, “hmm🤔, J=σE , where J and E are vectors. I need to multiply something to a vector which in result gives another vector that is not in the same direction. 1) If I multiply a scalar, resultant vector will be in the same direction. So σ is not a scalar. 2) If σ is a vector and we make a dot product, result will be a scalar. So it doesn't work. 3) If σ is a vector and we make a cross product, result will be a vector in the orthogonal direction of the given vector, which is not the case here. So it doesn't work either. 4) If σ is a 2×2 matrix, then the resultant vector can be in the direction other than the given vector. Therefore σ must be a 2×2 matrix.” Are my thoughts right? This is also my answer for the question at 7:35 We need 4 numbers to calculate the current density. Because a 2×2 matrix has 4 components. 33 Reply 2 replies @tiborkoos188 6 months ago The single absolute BEST explanation of tensors EVER. Period. Love it. 42 Reply @oakinger 18 hours ago thanks a lot for this explanation - I finally get at least the idea behind tensors! Reply @Mayank-v9p1g 5 months ago Your energy is infectious. I haven't felt this much fun in learning for a while. 2 Reply @eggfryrice350 7 months ago I got it in one go like ur explaination is so clear 😂 38 Reply 2 replies @shreenidhib314 7 months ago (edited) Please, 🙏, video on - 1. Geometric intuition behind COVARIANT and CONTRAVARIANT? 2. Where to use COVARIANT and CONTRAVARIANT? 3. Why GR uses COVARIANT form? 4. Geometric intuition for - Metric tensor, Riemann tensor, Ricci tensor, Christoffel symbols etc. 12 Reply @SecretAgentDharun 7 months ago I normally don't comment, but holy crap, this was an amazing video to intuitively motivate and define tensors. I wish I had this when I first learned about the conductivity tensor! 19 Reply @OrestiOS 11 days ago I love your energy and your teaching skills, this video really made me understand visually the key factors about tensors! Keep it up! 1 Reply @Impatient_Ape 5 months ago NOTE: The description of "tensors" given here is the classical physics/relativity and engineering use of the word "tensor". It is not the more general use of the word "tensor" in mathematics (or modern quantum mechanics), where the quantity of numbers in the multidimensional arrays are not just powers of "n". Also, in mathematics, the word "degree" is used to refer to the number of subscripts on the tensor elements, whereas this video uses the word "rank". Thus, a scalar is degree 0, a vector is degree 1, a matrix is degree 2, etc. To mathematicians, the word "rank" refers to spanning vector spaces, and in this context, it refers to the minimum number of "pure tensors" (which are rank 1) that need to be put in linear combination to create a given multidimensional array of values for a given tensor. So this means that in a mathematics context, a 2-dimensional NxN identity matrix is a rank-N tensor, but has degree 2. However, an NxN matrix where all the columns are just multiples of each other is a rank-1 tensor, but also has degree 2. 35 Reply 2 replies @Szergej33 7 months ago This is a very nice intuitive illustration, and I love the enthusiasm you have for explaining these topics with neat animations. It would be nice to have a follow-up where you actually explain what the difference between a matrix and a tensor is though, as it was really quickly glossed over at the end. I was that kid in school who thought I knew what a tensor was, just a generalised form of a vector/matrix. The thing is, all the examples you show for the rank 2 case only really illustrate how linear algebra and matrix multiplication can be used for physical equations. They don't motivate any distinction between a matrix and a tensor, so they don't actually let you intuitively understand what they are. Similarly for higher rank cases, any collection of numbers with n number of indices won't generally be a rank n tensor. I still enjoyed the video and I mean it as positive feedback, I hope you go a bit deeper into the explanation before / when you get to the GR applications you are planning to make a video about, as the distinction is a crucial point that lead to the field equations in the first place. 14 Reply @seedmole 7 months ago This all has very clear application in 3d animation and game design and such. Scalars intuitively can be used for things like scaling a model uniformly. But for operations like translations, non-uniform scaling, rotation, and other more obscure transformations, you need more data, be it a vector, or a matrix, or even such things as rank 3 tensors and beyond. Understanding this is an important part of why modern graphics equipment has hardware-level tensor processing units. 8 Reply @NAMITADALAL-pz9wj 7 months ago Your explanations are so intuitive, now I truly know what the heck is a tensor. 15 Reply @RoxanaLorenaD 3 months ago Yes, I'd like to hear more about tensors. All the topics you proposed at the end. 2 Reply @chuckjackson9393 4 months ago DUDE!!!! I have watched several videos on tensors but this video is the most intuitive description of what they are and why they matter. Thanks 3 Reply @SultanLaxeby 6 months ago This is spot on! Kudos to you for introducing tensors as multilinear machines, instead of "arrays of numbers which satisfy a certain transformation property" (which, unfortunately, is often how it gets taught to physics/engineering students). 13 Reply @nandu1770 7 months ago (edited) 23:18 heck yeah 31 Reply @Grandy_UiD 7 months ago Our boi is back. Blessings to the mom and child. 14 Reply @LionheartMaximus 2 days ago I knew the representation but this explanation makes it really easy to understand Reply @VaibhavKumar-zh5yu 13 days ago DAMNNN! That was good. Keep it up, man!👍👍 1 Reply @tzampini 7 months ago Excellent video. The best explanation of tensors I’ve seen anywhere. 😊 10 Reply @mandaglodon 7 months ago That was so INTUITIVE AND EASY TO UNDERSTAND!!! THANK YOU SO MUCH !! PLEASE MAKE FURTHER VIDEOS ON COVARIANT AND CONTRAVARIANT TENSORS AND EINSTEIN'S Field Equation!! 8 Reply @seatalknmeabridge 7 months ago Absolutely. We want to learn more about tensors. Please continue. Also with practical examples on how to use them and how to work with them . 6 Reply @robertweekes5783 1 month ago 16:00 to understand why angular momentum for most objects is different in different directions, imagine throwing a frisbee with a natural circular rotation — and imagine trying to spin it sideways, like flipping a coin. It takes more energy to flip it laterally because there is more mass resisting that change of direction, ignoring wind resistance. A homogenous sphere would have the same angular momentum in all 3 axis 2 Reply @tunapedia 5 months ago This is the best explanation of tensors I’ve heard so far. I’m a geophysicist and we deal with linear elasticity (rank 4 stiffness) all the time. Would have been really cool if you also showed symmetries and voight notation of writing out high dimensional tensors with symmetry! 2 Reply @tanush9773 7 months ago (edited) If anyone is still confused in why do we need 4 numbers in general . You can watch 3b1b essence of linear algebra series till ep 3. 13 Reply 6 replies @larsonfraud4156 7 months ago The most entertaining and down to earth explanation of tensors. Well done Sir! 5 Reply @rb9805 7 months ago (edited) Absolutely outstanding video And yes we want to understand the whole thing of general relativity with ricci tensor and einstein tensor and riemann tensor 31 Reply @redd1029 2 days ago I’m glad I found your channel gonna binge your videos. Reply @fawal.1997 5 months ago This story telling video format is genius. I usually watch concepts videos, somewhat understand it. Then, an hour later I do not remember anything. Kudos to you! 1 Reply @Vventure23 7 months ago ahhhhh you're back!!!! And your brain is working well enough to explain this, which is even more impressive. Super excited to see this :) 7 Reply @laurencehand12 6 months ago Finally, a clear introduction to tensors, clearly defining them and giving examples that are down to earth, describing stuff we know, and can be understood. Thank you! 4 Reply @cuneyitarkin1 7 months ago (edited) Students in maths (linear algebra) usually see that matrices of size nxm represents an (homo)morphism (a linear application from R^n to R^m). Working with the matrix is equivalent to working with the application. Vectors have coordinate in a basis. So the matrix is also expressed in 2 bases. Moving from one basis to the other has a formula. A tensor of order 2 is a matrix of size nxn. A tensor of order 1 is a vector. "Tensor" is just a generalization of a concept. The confusion (at least for me) is that instead of saying sigma is a linear application whose matrix is this in these bases we says it is a tensor. But we have never seen tensor in school. 12 Reply 12 replies @yuctoborian 3 months ago Magnificent as always. You put your X-factor personality together with your WHY-factor curiosity and understanding goes up a rank. 1 Reply @node6161 2 months ago Your enthusiasm and your explanations are exactly what we need Reply @BappiDebnath-qo3hn 7 months ago Sir finally you are back thank you 6 Reply @joeking4206 6 months ago (edited) Fantastic explanation and graphics. I am no mathematician but as a retired aeronautical engineer i am not completely ignorant of maths. At the age of 63 this stuff keeps my mind working. I am a huge fan of Richard Feynman and you did him proud. Also, I like your accent. Greetings from England. 6 Reply 1 reply @SM3502F2 4 months ago (edited) So it essentially means as the randomness of 2 or more acting factors increases, so does increase the tensor ranks. A scalar would be a point in time, i.e. where there is 0 randomness, vector when that point starts traversing i.e. randomness pushing in 1 single direction in whichever plane it clould be, r2 tensor when the point starts spinning i.e. randonmess in twin direction in whichever plane it could be, r3 tensor when the point starts inertwining, i.e. randomness in thrine directions and the intertwined force defining the direction in whichever plane it could be.. This implies with each increasing rank or in other words randomness of the interacting forces, the complexity of intertwining forces increases which ultimately in aggregation defines the direction of the movement of the point in whichever plane it could be.. Stretching the theorem to infinity, it can therefore be understood that as the rank of the tensor increases towards infinity, or in other words randomness of the interacting factors with each other increases to infinity, it would reach a point where the point remains stationary and is unable to move because the randomness of the factor perfectly cancel each other or dont affect the movement at all.. this implies that the point or scalar is by itself also a rank infinite tensor, that refuses to budge because the randomness of the force reach infinite or in other words they no longer have the ability to affect the movement of the point.. Full circle.. Also it implies 1 thing any proportionality between 2 or more interacting forces or factors can be equated by introducing a variable instead of a constant, which would be product of the constant and randomness of the interacting forces or factors.. or say R factor. This also implies another thing that between 2 or more interacting forces or factors, as the randomness of the interaction is introduced, the fundamental nature of the factor or force even though remaining same, results in as many product of the factor or force - meaning fundamental forces or n0 tensors are the true units of all forces or factors.. 3 Reply @garybender3684 1 month ago I also loved the Feynman touch. I was fortunate that I had the opportunity to attend a series of his lecture on Quantum Electrodynamics, He was so good that he convinced me that I understood it. 1 Reply @RaptorMaitre 8 days ago When I was in my first year of engineering, i always struggled with Matrices but as soon as I started visualising tensors, it all started making sense and I never had a problem after that. Sadly, being a computer engineer, i somehow forgot all this as I never really needed this. Watching this video, it all came back to me, so thank you for this. I suppose I'm going to use this again in the quantum computing in near future. Reply @JustARandomUsername2137 7 months ago I didn't understand tensors at all before, but now they seem kind of obvious. In fact, I think I might have accidently "discovered" them on my own, just didn't know they are called tensors. 4 Reply @asandax6 6 months ago (edited) 9:04 My intuition said 4 right at this moment. The reason is because I remembered a lecture by Freya Holmer "How to multiply two vectors". Where the components of the vectors ended up having 4 unique terms that prevented the vectors from becoming just one simple number. It's amazing how mathematics connects everything as in this case were talking about elctricity but freya was talking about video games specifically graphics. Edit: I highly recommend watching Freya Holmer videos even if you aren't interested in video games and just interested in math. Most math concepts I didn't understand became clear after watching them. 5 Reply 2 replies @brycon1277 5 months ago Your excitement about this topic has actually re-engaged me in understanding physics. I can't express how much this means to me, but seriously, just watching this video has made me so excited to learn more about math and physics and the universe, and I feel like that type of knowledge is going to allow me to explore the stuff that I feel truly matters. Thank you so much for making this video and having you're curious, excited attitude towards it! It really reaches me in a way that I haven't found for a long time :) 4 Reply 1 reply @PradeepLakshmiNarasimha 4 months ago For the first time, I watched an entire physics-related video and I have to say, you did an exceptionally good job explaining the concept! 1 Reply @ninaaddesai4814 6 months ago (edited) I've been trying to understand tensors for almost 2 years and I wasn't able to find great content or resources that provided me an intuitive understanding of this concept, until I watched this video. For the first time, I was able to intuitively understand the concept of precession as it is a consequence of the generalized moment of inertia tensor. Thank you for making such great content and good luck to all of your future projects. 2 Reply @JoaoSilva-bv3ch 7 months ago Thank you :) You're my favorite youtuber teacher :) 5 Reply @gr8points17 7 months ago (edited) 19:33. You can also call that "elastic constant" Young's Modulus. And for liquids, the "Bulk Modulus" (Volumetric Stress/Volumetric Strain) is usually what we're talking about. Since you mentioned crystals, Young's Modulus (Gamma) might be an even better fit there, but no biggie! Anyway, really enjoyed the video – tensors have always fascinated me! Thanks for making it! 6 Reply 2 replies @RawleyGreene 2 months ago I have a PhD in Materials Science and didn't quite get the origin tensors until I watched this. Even after dealing with stress as a tensor, and the stiffness and compliance matrices. Great job! 7 Reply @Clashar 3 months ago Please continue with lessons, you have such a unique friendly way to teach complex things in simple way! Reply @walterhfs 1 month ago Man, thank you for such a quality video. I'm always glad when I hear real voices from creators these days. 1 Reply @yassine-sa 5 months ago 20:02 rank 4? Why! If e was n² it would be a matrix and won't multiplication of two matrices give us a matrix and solve this?! If what you're saying is right it's probably because the multiplication is not a simple matrix multiplication and it's some other type of multiplication, which you didn't define so that example is not valid 10 Reply 4 replies @Sreejith_37 7 months ago How dare youtube hide this from me for 1 minute? 5 Reply 1 reply @misterlau5246 6 months ago 13:54 🤣💪🤓 YOU CHEATED🤣🤣🤣 3 Reply @swimneo 5 months ago Found you by accident. I love this level of complexity explained with your style. You have a real gift sir! 1 Reply @geoffreynorth9046 2 months ago This is brilliant... the best explanation of tensors I have ever come across - the first to give a proper intuitive understanding - thank you ! 1 Reply @Md_Sirajul_Basir 6 months ago (edited) 11:27 Earlier we "just got lucky" because our axes (basis vectors) were along the eigenvectors of the matrix. As we know eigenvectors of a matrix are special directions along which any vector only gets scaled (stretched or squeezed), but never gets its direction changed, when subjected to a linear transformation by the same matrix. The scaling factor is determined by the corresponding eigenvalue. And if we take our basis vectors along the eigenvectors of a matrix, the matrix becomes diagonalized (all non-diagonal components are zero).That was our case earlier for the anisotropic crystal, and that's why we needed only two numbers, only the diagonal components. 11 Reply @Reaction1s 5 months ago Most of material science deals with what you are saying @3:24. 3 Reply 1 reply @themaster8405 7 months ago So tensors are “just matrices” and “multilinear machines”? That’s a dangerously shallow take. A matrix is only a tensor if it transforms correctly under a change of basis—something this video barely hints at. Tensors aren’t about the number of components; they’re about how those components transform. Stripping away that core idea and calling it “intuitive” is like explaining gravity without mass. It's not intuition—it's misinformation wrapped in enthusiasm. Also the idea that “misalignment between vectors implies a tensor” is oversimplified. 4 Reply 1 reply @kingsimx 5 months ago bro the way you hold a conversation with a paper! the way you talk to one of the greatest minds, in a way we can understand! amazing! 1 Reply @CalNx-l3t 2 weeks ago (edited) It seems like this problem can be considered as a linear transformation in linear algebra. 1 Reply @HusseinBoris-mr8xi 2 months ago The glazing here is crazy 😭😭✌️ 4 Reply @David-w7w2q 1 month ago Your enthusiasm and obvious love of your field makes you a particularly effective educator. Brilliant job...thanks much for making the world a bit brighter. Reply @wyncudlip6134 3 months ago Glad I eventually came across this. A great explanation about something I have always puzzled over. Reply @justbill95staufer18 6 months ago Love how you share your „Eureka!“-moments with us 😊 another great explanation!! Keep it up 👍 2 Reply @tttm99 2 months ago Easily the best description of the generalisation required from simple single direction equations to the real world, putting tensors in context intuitively and by example. My new go-to for the explanation and an instant subscription in the process. 👍 Reply @Paul-ks2fv 1 month ago The bongo player has been one of my heroes since came across him in 80s 1 Reply @JohnNelsonNumber2 4 months ago Finally! A simplified explanation of tensors! Reply @martinsanchez-hw4fi 4 months ago What did you use for the animations? Very cool video 1 Reply @mad-pj 1 month ago tensors are such a brilliantly beautiful "simple" concept. Really makes the blocks make sense. Reply @user-sb3wh3dd4v 4 weeks ago Excellent lesson ! Great graphics. Clear explanation. It was your enthusiasm that sold it for me. Very few know the genuine excitement mathematicians experience when we suddenly understand something. It's like seeing something immensely beautiful for the first time. Reply @PulseInterstellar 3 months ago I've been chasing this question for years, and I think you will finally end the quest, once I fully absorb all this. Thank you Mahesh. Reply @DrPG199 6 months ago You have by far the best explanation of what a tensor is. Congratulations! 1 Reply @edvogel56 2 months ago Please do continue this series on tensors! Reply @schrodingerscat1863 2 months ago Easily one of the best explanations of tensors without even defining a general concept it gives a clear understanding of application making it more easily to visualise. Feynman was an absolute genius not only in his understanding of such concepts but more importantly in being able to explain them to others in reference to something else they could understand. I once saw an interview with him where he explained to the interviewer that he couldn't explain a concept to him because there was no frame of reference it could be conceptualised in that the interviewer would understand. Such a great answer. Reply @chad872 1 month ago it makes me so happy to see this channel grow... Reply @krishnachaitanya6800 2 weeks ago Thus is great Mahesh! proper intuition Reply @kantimakan4056 11 days ago Thanks for this enlightening video Brilliantly explained Reply @AAlok_Yadav_AA 2 months ago Yes make those videos, waiting impatient for them Reply @vishank7 4 months ago You're the guy from Khan Academy! I loved watching your semiconductor videos there a few years back - so good to see you succeeding on your own channel!! 1 Reply @jojog8304 5 months ago Nicely done. A lot of professors have use this example, but haven't seen it in a video yet. Reply @garygrebus1602 5 months ago Great graphics! Great pacing! Great enthusiasm! This was really helpful. Reply @douglasstrother6584 5 months ago Landau & Lifshitz present a "different angle" on Physics. "Electrodynamics of Continuous Media", Vol. 8, is one of my favorites: it brings together electrodynamics, continuum mechanics and thermodynamics. Section 10 "Thermodynamic relations for a dielectric in an electric field" and the following sections give a unique perspective on dielectric behavior. It also covers anisotropic and non-linear materials. 1 Reply @aiSage48 1 month ago If they gave this explanation on Day 1 of the Linear Algebra course, I'd be hooked. Reply @DanBRZs 5 months ago i wish all professors had the same enthusiasm and didatics that you do Reply @Albtraum_TDDC 6 months ago Your example with the orbiting satellite reminded me of the weird rotational oddities. Like this video by Veritasium: Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation. Also explained in Dr. Shane Ross: Dual-Spin Spacecraft | Instability of Intermediate and Minimum Principal Axes for Free Rigid Bodies 1 Reply @CriptoKnyght 5 months ago You really make this fun. Well done. Reply @Anime_forlife2 4 days ago You got a new subscriber. Love it Reply @darkside3ng 3 weeks ago This is something else. I really love your explanation and how do you get the right point. Thank you so much for your effort and detailed illustration of your understanding. Reply @Xeanos583 3 months ago I've spent some time doing graphics programming, and in it we have lots of vector transformations that need to be done for various effects and simulations. Matrices are used to transform vectors. I somehow made the connection that the (Emf)vector needed to be "transformed" into the (J)vector, and therefore concluded that we'd need a 2x2 matrix, or 4 numbers to correctly describe sigma. Turns out my experience paid off, and I was totally correct! 1 Reply @saliherayman4205 2 months ago Bro i was studying on that solenoid valve design, i am an electrical&electronics enginering 4th grade student, and i just discovered you for to learn what the tensor is? You are the BEST man!! Reply @Arkhs 3 months ago This is great, going to have to come back to it again and work through some examples to truly say I've grasped it. Thanks buddy. Reply @kevinmacharia4295 10 days ago Holy flip, I just understood WHAT conductivity is!!!! Thanks dude, subscription earned. Reply @jordyb4862 4 months ago Amazing to see high animation quality exploring topics in this level of detail 👏👏 Great job!! Reply @mfadhilal-fatih1427 1 month ago So tensor are a form of value that transform a vector input direction.. in math language it's a matrix transformation function. So interesting that such concept also exist on a real natural phenomenon 2 Reply @7enshie 2 weeks ago i wish i had your attitude towards my studies Reply @ForeverGTTK 5 months ago blows my mind, such simple explanation for a complex and high level mathematical idea, you are amazing ! Reply @LiliekHandjoko 1 month ago ​"My thesis when I was in college was about the application of tensors for the analysis of electrical machine performance (motors, generators, transformers, etc.). ​Using tensors, it's possible to perform a simultaneous analysis of electromagnetic, mechanical, thermal (and even financial) quantities from several machines within a network. ​Tensors greatly help in understanding the characteristics of the overall system." Reply @Androxylo 1 month ago This was so beautiful, thank you Reply @RustyJalopy 5 months ago (edited) This is the best explanation of tensors I've heard. Thanks, Mahesh! Reply @anoopramakrishna 3 months ago Very intuitive! Do spinors next! Reply @SaiGollapudi-f1w 2 months ago Thanks for your enthusiastic explanation. It was very helpful. Appreciate it. Reply @atgabs 5 months ago Well, the way you explain kinda made me feel optimistic about next semester... Great delivery! Reply @meabh00 3 months ago The beauty of teaching and learning is when someone not only teaches you the concepts, but also shares their passion for the subject. Keep going!! ❤🌟 Reply @jalexcrockett 5 months ago Love the approach to understanding. Very cool. Reply @PanduPoluan 2 months ago Whoa, nice introduction to tensors! Thanks! Reply @DavidBealesLeeds 3 months ago Explaining scalars as rank 0 tensors, and vectors as rank 1 tensors was very helpful. Reply @yiwmsh4393 5 months ago I adore your enthusiasm for learning! Reply @93lozfan 4 months ago I made it through 4 year of engineering school hearing the word tensor and not one instructor explained what it was. I've been in the field working for 5 years and finally i might learn what a tensor is Reply 1 reply @hey.uxdr_7 4 months ago the best video on internet about tensor really enjoyed it Reply @JulieanGalak 2 months ago (edited) I first encountered tensor in electrodynamics, and absolutely couldn't figure them out. Some video or article about tensor pointed me at mechanics, where tensors are used for stress, and for some reason that made much more immediate sense to me (even though I have a lot more background in EM than in mechanics). I was then able to transfer that back to this type of problem. Your explanation is very good, if I saw it back then, I might have avoided the detour to mechanics. :) Reply @ValleysOfNeptune2150 4 days ago Great 😃 thanks for your work Reply @TITANIUM_POTATO 3 weeks ago Bro my exam is like in 20 days and you came in clutch Tnx for the video Reply @pbezunartea 5 months ago Your enthusiasm is contagious! Great video. Reply @antonioalvez1562 5 months ago I have to say that i really like your enthusiasm towards this topic, its really contagious. Keep doing this type of content, i find very genuine to see how much you like it! Reply @douglasstrother6584 5 months ago My favorite is the Maxwell Stress Tensor, because electromagnetism isn't stressful enough without it. 1 Reply @dirk11050563 3 months ago Dude... Best explanation i have seen so far... Really really good. Thank you very much for this! Reply @taranimallik 2 months ago Amazing way to explain the concepts. Thanks. Reply @fusion2x 5 months ago If only all teachers were just as enthusiastic as you, this is addictive. Love your work! Reply @lambda_calc 5 months ago I love the clarity of this explanation. Your enthusiasm is infectious and the way you frame this as a conversation with Feynman gives it a narrative quality that makes it fun to follow and easy to share the "light bulb moment". Thanks for posting this! Reply @SurawutAnurak 3 months ago My head hurts, but your energy keeps me watching. Reply @KoniiTweet 1 month ago (edited) Finally The algorithm brought me to your channel 😍 This should've been happening many years earlier but here I am. Thank you for your work, it's a pleasure to see some being so excited to talk about a topic. Reply @realkanavdhawan 4 months ago Great Information on Tensor The summary Two proportional tensors of rank n when not aligned to each other in space leads to proportional constant an another tensor of rank n² Each component of L.H.S Tensor will be represented by linear combination of components proportionality tensor and R.H.S tensor Examples of tensor Conductivity Stress Strain Modulus of Elasticity Angular Momentum 2 Reply @hcoster 2 months ago Great video with a really good fundamental explanation of not only what a tensor is, but also why we need them to describe even simnp0le physical phenomena. I love your enthusiasm! Reply @dngo2991 5 months ago The best explanation of a tensor on the internet that I've ever seen. Bravo! Reply @LouisCheungCN 4 months ago Please, more videos like this one. Your videos are interesting and energetic. Thank you! Thank you! Reply @KFRogers263 6 months ago would love to see more on this! Reply @MrKelaher 2 months ago I love your enthusiasm and joy :) Reply @lalitasharma6687 3 months ago As a Chemistry student it's Worth watching thanks 🙏 1 Reply @billysgeo 5 days ago Feynman blowing minds decades after he’s gone! What a legend! Reply @kunjupulla 4 months ago (edited) I had a material science (not my main subject) professor in 1st yr of engineering who used to quote Feynman's works and methods. It actually laid a solid foundation on my intuitive understanding of semiconductors! You quoting Feynman reminded me of the prof 😊. Reply @jsz4tube 4 months ago Thanks a lot! I grasped it. Feynman's lectures & your visuals & enthusiasm are great dope 😉 Reply @TIO540S1 4 months ago This was really a very good video, and I love your obvious enthusiasm. Reply @jay_wright_thats_right 1 month ago i have no idea about what you're talking about but you're entertaining. thanks for your hard work. Reply @vh8413 5 months ago finally someone to explain it to me in such a way that I can understand it! I've been working on this for a while but no, I didn't understand it, thanks my friend! Reply @michihyde8433 2 months ago Wow, this video was amazing, thank you so much! How you pull all these areas together gives a very intuitive understanding of this structure. Perfect examples! :) Reply @__-1234 2 months ago This is the best explanation I found so far. Also it made me realise that as Monsieur Jourdain, I have been using tensors for years without knowing it. Reply @MisterTrayser 5 months ago The amount of joy of this man is what everybody should get in life Reply @ianjaeger 5 months ago Haha, I love how excited you are about this! This was one of the things (among many!) that I just had to memorize rather than understand when I got my engineering degree 20+ years ago. 20 years later, and some of the things I was taught in my Ceramics Engineering degree finally make sense!! (piezoelectric for example!). Thanks! Reply @fhjcsadgk1 5 months ago thank you!!!!!! i did not watch it yet but omg this was recommended to me after our qm prof starting using tensors without any introduction or explanation of what they were Reply @christopherweigand7518 3 months ago I tried to avoid some of your content as i thought i was scratching my math, physics, and science itches with other channels and media materials. I'm happy to report your damn enthusiasm for these absolutely difficult subjects has sucked me in and i'm hooked. That is the closest i've came to understanding something that does not make intuitive sense. Love the use of Fenyman's lectures. Reply @heliosobsidian 5 months ago I like you reaction on explaining Tensor! Thank you so much for this clear and intuitive explanation. Reply @Groot-P 4 months ago Your explanation method is really cool! it is intuitive Reply @LilForklift 4 months ago Bro your content is actually top tier. Reply @aminenoob9011 3 months ago this is the most genuis explication i ever seen. Thank you so much Reply @candidmoe8741 2 months ago Understanding tensors was always on my bucket list. The math seemed complex and abstract, but with your video, I finally understood what it was all about. Now I can die in peace. Thanks you very much. Reply @brownie0710 5 months ago In my first semester in university, our physics teacher was presenting the course to us reading the syllabus and somehow started talking about tensors. Keep in mind, this was a physics fundamentals class, we barely even knew what a vector was (yes, we had terrible high school teachers). My friend and I walk out of class without even understanding a word the teacher had said and it began a inside joke between us to talk about tensors. If someone asked us what will be evaluated in the next exam we said tensors and burst out laughing. Discovering that vectors and even scalars were a class of tensors its kinda funny. This happened 5 years ago, my friend change university because of academic trouble and I kept pushing as hard as I could to pass de classes of my career. Now I am one year away from graduating and this video brought back some memories. Some very happy memories. Good vid, keep up the great work! Reply @MeowMeow2718-z5e 2 months ago This is a nice fresh perspective on the physical justification for tensors. I've looked at tensors only really through a differential geometry perspective which is ofc pretty abstract. So it was nice to see some physical argumentation for the usefulness of tensors. Good comment at the end suggesting coordinate invariant approaches too! Excellent educational video! Reply @null_s3t 4 months ago Mahesh, you are a very special kind of educator. Never stop being you and keep up the good work. Great video as always, tensors and differential geometry can be very challenging to understand intuitively. 1 Reply 1 reply @DaveRoberts308 5 months ago Nicely done. So often, physics gets buried under a heap of unintelligible equations. I love how you drove it intuitionally. More, please. Reply @danlegenthal6167 3 months ago I studied ECE. You explained tensors better than any of my professors ever did. Bravo! Reply @opolo704 5 months ago This is what makes you one of the best teachers. You REDISCOVER the concept. It is by giving you the situation and the question that prompted the invention of these things that they actually start making sense. When they just explain to you the definition and tell you that it's used here and here, with these more advanced concepts you just can't see the direct connection that easily. Reply @realmetatron 2 months ago (edited) TLDR: A current in x direction also induces currents in y and z direction, so you need 3 numbers for the current in x and its effect on y, and z. For current in y and z it's the same, needing 3 numbers due to their induction of currents in the other directions. This totals 9. 2 Reply @atmosphererobinhood6920 4 months ago Thank you! I'm totally new to the concept, which is actually kinda hard, but your inspiration is contagious! And it burns out a fear to bring a clear light of knowledge! Wish you keep your enlightened sight of view and motivation to share it. Reply @Debraj1978 5 months ago I am watching your video for the first time and its awesome. Your enthusiasm is great and kudo to 400K+ subscriber on Physics. These are real subscriber who understand your explanation and want more. Reply @Umar_JS 4 months ago One thing I like about this channel is the “rediscovery” thing. Even if I don’t understand anything beforehand, I can still watch the video. Reply @wittymaximus 3 weeks ago (edited) Such a complex topic made so simple...intuitively! 🎉 Yes, it's a lot simpler (not easier) to comprehend tensors now! Thank you for the wonderful content....kudos to the creative thinking behind the simplification efforts! The comments section is equally amazing. There're many, one worth mentioning is a comment on eigenvectors and further comments on it on extending eigenvalues to include complex numbers... grateful! Reply @xreak 5 months ago Inspired learning! I especially liked how you incorporated that story with Dr. Feynman. Keep up the great work! Reply @bathtubearth8252 6 months ago Your enthusiasm is infectious 🙏 Reply @SparkyFinch 5 months ago I have no idea what's going on but I'm glad it makes you so happy Reply @BharathBhushanLohray 5 months ago A video on multi sorted Algebra would be nice. What are they? Why do we need them? Where are they used? Reply @artabinkabir2908 1 month ago Make a play list on Tensor. Please. Reply @MorningbirdSpaceCorporation 3 months ago You're delivery, sir, is awesome. Reply @synchromesh 2 months ago That was great! If you could do a similar explainer video for quaternions that would be awesome. Thanks for making these videos! Reply @nikolayhmn 2 months ago thats passion if i've ever seen it Reply @DAN_keep_believing 2 months ago I needed this video during my JEE study days Reply @AllAmericanBeaner68 6 months ago This profound and very intuitive approach to tensors not only added to my perspective on the subject, but earned yourself another subscriber! Reply @jojog8304 5 months ago (edited) Boom goes the Tensors. Great job in visuals. Great to point out that linearity is very important concept. Reply @phinsenrenaldo1304 5 months ago Hi, wonderful video by the way. I was wondering... what did you use for the illustration to explain those equations? Did you use an app, or was it a full-blown animation/picture/illustration you used by using let's say illustrator or smth. I'm a teacher and it seems like having that knowledge/tools would really up my game in explaining to my students. Does anyone else have any idea what might be used here? 1 Reply @sambeard4428 3 months ago I love your enthusiasm Reply @LOLWUT281 6 months ago I gotta admit you blew my mind. Never seen your videos before. Subscribed. Reply @MicahSue 5 months ago My goodness, this video is a wonderful explanation of Tesnors! Reply @ElvisRandomVideos 5 months ago The way you teach is pretty amazing, looking at the root of the problem instead of just assuming everyone knows all there is to know. Reply @elmo2you 5 months ago Being a good educator is something that takes a lot of skill, often talent, and certainly does not come as easy as the end results do to consumers. It is great to see people taking Feynman's brilliance as a base for their educational material today. I'm convinced he would have loved to see this video, with modern technology enriching the presentation of his ideas. Sir, please consider yourself a great educator too, you did a great job with this. Reply @walterhughes7763 6 months ago One of the most interesting "dense" videos i've ever seen. Instant subscribe! Reply @dantong5623 2 months ago The linear machine definition of tensor is also the one explicitly discussed in the Misner Thorne and Wheeler's book Gravitation. It was extremely intuitive for me right from the start. Also don't think of the input as a vector and output as another vector. Tensors take in a set number of vectors and one forms and give you a scalar, in a linear way! Reply @franciumruel615 5 months ago I never understood tensors in my undergrad mechanical engineering. When I took Advanced Mechanics of Fluids in grad school, where the professor was just so amazing and taught a lot of tensor calculus; it was only then that I finally understood them! To be honest, I find the index/Einstein notation very intuitive now. Reply @mathedguy 1 month ago Excellent video ! Informative and fun ; thanks ! Reply @XDicer 4 months ago Excellent video, I look forward to more videos about tensors Reply @krish_iitkanpur333 5 months ago best video I have seen FOR INTIUAITON BUILDING Reply @shrihanreddykypu2089 6 months ago Can you please make videos on Schrödinger's equation and how to draw graphs, and a part 2 on tensors about how the field equations work and more as your the only one who can do this properly and understandably Reply @PelleStorck 1 month ago Great channel! Glad i found it. Reply @michaelschnell5633 3 months ago Many thanks ! Of course more intuitive insight on tensors is very welcome. It will be very interesting to see if there are ways to intuitively visualize stuff like covectors, upper/lower indices of tensors, lowering indices. Reply @hughatkins 1 month ago Very nice explanation. Thank You! Your enthusiasm and ability to lead me through a thought train to realization is more than just explaining. I enjoyed your video. Reply @damien44mjfan 5 months ago You know what I love the most in your videos? You really look thrilled by the math you explain :) <3 Reply @Professor91811 2 months ago I have nothing to do with tensors but your electrifying enthusiasm kept me going. Damn only if my teachers were this fun Reply @the_truth_seeker334 3 months ago I was searching about the vector database and landed here and I learned something that is very useful in my subject. Until now, I was using tensors without even knowing what it is. Today, I got lucky. Reply @kabitakumari230 3 months ago 3:24 ❤ Went to revisit my class notes on dc circuits about current density in terms of charge per unit volume,drift velocity and in terms of specific charge of electron(charge/mass),charge per unit colume and average collision time of electron in the conductor. Now I have a better clarity and interconnectedness Reply @yaghogrossi7947 2 months ago Fantastic vid, my friend! Love your enthusiasm! Godspeed! Reply @user-rm2qj2jh4l 4 months ago Wonderful, illuminating video! I love you enthusiasm. Thank you! Reply @randyscorner9434 6 months ago Nicely done. WE all need good mental models to understand such abstract constructs. 1 Reply @nutronstar45 3 months ago This is incredibly informative, well done! I'm kinda dissapointed that you didn't mention tensors that take in multiple parameters, like the inner product or the cross product. Reply @shenoyroopesh 3 weeks ago Wow, I've only ever heard the word "tensor" before, now I actually understand it! Reply @miramavensub 3 months ago My shortcut was realizing that tensors describe how the space the model is in affects the results. So if you think about a pendulum on a string over a parabola, the pendulum will be slowed down by the parabola as it reaches it and has to climb up, then sped up as it descends the other side. If you just use a normal pendulum model it will break, so the parabolic space is described by using a tensor to adjust the contours of the model to match the space it's interacting with. Reply @chiraldude 5 months ago Thanks for crediting Feynman. He wasn't the most brilliant physicist but he had a special gift few scientists have. He was able to explain the science in ways that are understandable to us regular people. 1 Reply 1 reply @jeffreyplett5984 2 months ago These animations are incredibly helpful for visualizing what is going on! Where can I learn how to make animations like this myself? Reply @ericneckel8646 2 months ago Perfected presentation my Brother !!! I love to learn to learn. You, I see you have that same spirit, pure wellness. The current generation has so much at their fingertips. This reminds me of studying light theory in the mid-1980s, impregnating light with sound in the human spectrum using a speaker glued on a mirror playing music. I then used a photo sensitive transistor in a simple 3 chip circuit and other accompanying components to cancel out all other frequencies, other than the human spectrum which left me with the music and my conversation around the mirror! It brought the same smile on my face as yours... This led me to "Twisted-Light" theory and scaler wave thoughts without even naming it scaler, I saw light in another way for the first time, in multi-dimensional form. Others have picked up this knowledge and ran with it. They used a sample of used automotive foam out of a seat and recovered the sound it was exposed to throughout it's lifetime !!! YES, to most, that sounds impossible after the thought of scary. Water carries the same as observed by breaking the hydrogen bond in the process known as cavitation, when light and gas are emitted, carrying on the frequencies it was exposed to after bonding hydrogen and oxygen forming water. You see how you just affected me in such a beautiful, profound way? I Thank You. Reply @Zero-yu7fn 6 months ago The quality of these videos have gone up. And I'm still loving them the way I did when you started this initiative. Love you content Mahesh sir! Reply @alice20001 4 months ago I LOVE this style of teaching <3 Reply @jhmilan 2 months ago One of your most amazing videos. Thank you 😊 Reply @kongolandwalker 5 months ago 16:00 horisontal component of omega should have had an arrow, representing the rotation, in the other direction, to match the right-hand rule. 1 Reply @JoeBorrello 5 months ago That was a great explanation, thank you. 😊 Reply @yolanankaine6063 2 months ago Blown my mind. This has finally clicked for me, thank you! Reply @perfectmovementchannel7838 3 months ago please bring next videon on vector 1 Reply @ThatNateGuy 4 months ago I'm still blown away that the Higgs field in QFT is a scalar rather than a vector. Reply @theotherguyhere 1 month ago Amazing explanation, thank you for making it Reply @GeezusCheezus 2 months ago Amazing video which explained a lot of stuff I didn't previously understand about Tensors! I do have one addition/nitpick though, mass is only a scalar in Euclidean coordinates. Once you transform into polar coordinates for example and calculate kinetic energy, your mass matrix will no longer be just a scalar! Reply @austink4318 5 months ago The Riemann Curvature tensor is still an enigma to me, any content delving into it would be greatly appreciated. Reply 1 reply @rsovat 3 months ago Excellent video. Thank you for your time and work. Reply @Garfield_Minecraft 6 months ago so it's just multidimensional array?(as programmers call them) 1 Reply 1 reply @Swannilization 5 months ago (edited) This video is amazing, brought it all together for me- never connected that asymmetrical components not set up on nice axes might increase the rank of the tensor calculations. Reply @thejoojoo9999 5 months ago Great video, love your enthusiasm. Reply @dylanfinlayson5556 3 months ago I had the same mind blown moment you described watching your video. Then I got really mad that I had never heard them explained so simply before. I've even used rank 2 tensors before, I just didn't know that's what I was doing. Reply @zetacrucis681 1 month ago Nice one. Feynman ftw! I've never read the chapter on tensors but I'll have to now... Just one thing worth noting: for the 2D case 7:28, while indeed one number (or two if sigma_x, and sigma_y are both non-zero) is not enough, we don't need 4 numbers either. Three are enough: the angle specifying the orientation of the coordinate axes, and the conductivities sigma_x and sigma_y along the "principal"/special axes. A bit of trig and algebra shows that the conductivity tensor with respect to the rotated axes will be symmetric with sigma_xy = sigma_yx, which confirms that we only need 3 numbers here. More generally, in N-dimensions, we need N numbers for the conductivities along the N "special" axes, plus N*(N-1)/2 angles for the orientation (N-1 angles for the first axis, N-2 for the second, ..., 0 for the Nth), i.e., N*(N+1)/2 rather than N^2 numbers in total. Again, this checks out if the conductivity tensor is symmetric. Reply @madmaxfzz 5 months ago Very, very cool! I've always had a little trouble visualizing tensors. 3D Vectors and fields and gradients and stuff I could always picture in my mind and allow me to remember somewhat complex relationships, but tensors always teased me by staying just at the edge of my full comprehension. Over time, I've seen different explanations and I've slowly come to understand them on a more visceral and with a more complete and usable mental picture. This video has added to that structure of knowldge. I appreciate it! Reply @UziMusic 4 months ago I remember I was super stressed out dealing with these at I'm assuming a basic level in solid mechanics. But they're so much more interesting without time crunch to visualize like you have here, great work mate Reply @amanofnoreputation2164 5 months ago (edited) The way I'd put it is that tensors are a reducing function "reducing" here meaning to simplify in the same way that a formula allows you to work out all of the points that a given line will pass though: As long as you have the template, you can elaborate the full pattern; you don't need to measure or plot them out manually. The more dimensions you need to reduce from to get your co-efficient, the higher the rank of the tensor. You're taking any combination of intensity and direction across two variables and distilling it down to one value which defines the relationship between the variables. Reply @opaboba 5 months ago 😭why u explained - so... good... My eyes literally are filled with tears, right now. My God !! I finally get it 🤎 1 Reply @Pierre-Lin 2 months ago This is very useful. Iʼm going to share. Reply @ridhaaloina 3 months ago due to your excitement of teaching and so much positive energy, I never realized I finished watching physics education content for about half an hour 😅 it is refreshing and fun even though I graduated from college 4 years ago 😂 Reply @MotorsportsTamizhil 4 months ago Yes, I need more intuitive videos on Tensors Reply 1 reply @herrefaber6600 5 months ago This was a really really good video. Thanks. Reply @RDS220-VX 6 months ago can you please do a video on electromagnetic waves ? 1 Reply @anasterisk15 4 months ago Hell of an explanation bud ! You won me ! Reply @sanjay98317 2 months ago Superb explanation, Mahesh. Reply @SujeeshJohn 5 months ago Bhai... Thank you for breaking this up in a way that makes sense.. Reply @ivanbukac4618 6 months ago Tensors confused me a lot. But after this I understood that I knew them all along, the vector decompression and how it works. Thank you for clarifying it. Now I know what they mean by tensors for the first time. Reply @niteman555 5 months ago Thanks for sharing; this makes everything super clear. I imagine that in certain cases, rotations or edge cases can reduce the tensors to just single elements or vectors Reply @earthscrust9092 2 months ago Thank you, finally, it made sense. Reply @Nopurpose-q4l 1 month ago Equation of torque with inertia being a matrix was first i learned about tensor Reply @Abdo_Elawady 5 months ago wow! as an engineering student who is passionate about mathematics, I wanted to understand tensors but I've never understood it from any source other than this amazing video... well explained and precise. Thank you!! Reply @mathiastan1975 5 months ago Great explanation!! As always!!! Your way of explaining is genius!! With so much enthusiasm and didactically excellence!!! It is always a pleasure to watch your videos!!!!! Thank you so much for all these enlightening moments!!! Reply @OfNoTrades 3 months ago Thank you so much for this. Tensors FINALLY make sense! Reply @russedmonds227 5 months ago This is a great video! thanks for posting this. Reply @shadew04 3 months ago THANK YOU 1 Reply @BertHeymans 5 months ago Super explanation, thank you! Reply @luisthoppil6163 6 months ago Genuinely amazing video. Please lets see those videos on metric, Einstein and rank 4 tensors 🙏🙏 Reply @achillev61 6 months ago Mahesh you're a great! I studies theories of tensors but for first tima i understood the physical meaning. Thankyou so much! Reply @xzaratulx 5 months ago Very nice and clear explanation. thx ! Reply @harshkumarsingh3418 5 months ago i am lucky to find this video 🥺best explanation so far on youtube. You explained exactly to all the questions arising in my head. Reply @carywalker7662 4 months ago Infectious enthusiasm!!! Reply @Ikkarson 6 months ago Thanks, I knew quite a lot about tensors already, now I have an intuition for tenzors 😉 Reply @NicolasGreg 6 months ago Thank you so much. At last i have a clue about tensors. Reply @mpalin11 5 months ago (edited) This is really great stuff 👍 It was the idea that the two things could be in different directions, that blew my mind 😊 Reply @thecompanioncube4211 4 months ago As a mechanical engineer by education, this is delight to see someone understand the underlying mechanisms of tensors. They’re very vague and abstract, but are magical and backbone of all our mechanical structures Reply @maximuslord8058 2 months ago Well explained, bravo 👏 Reply @CypressVintage 3 months ago Exceptional. Well done. Reply @farhan-momin 5 months ago (edited) Great, i was stuck at 10:21 for a lot of time. Since till this point we were only assuming the electric field to be in a single direction. and now mahesh introduced Ey direction so i was confused. then i input the conductivity tensor given by him in gemini, and it explained to me why Ex and Ey are considered. its because in a material, the current density vector can be derived for electric field in any direction Ek. This Ek vector can be then represented in form Ex and Ey and this can be plugged in Conductivity tenor to get the direction of Jk produced for Ek. This Jk is in the for Jx and Jy in the tensor. Edit: this is for anisotropic materials in 2D. moral of the story for any direction of electric field Ek, decompose it in 2 vectors Ex and Ey 1 Reply @armando-goncalves 5 months ago Mahesh thank you for your contributions to keep Physics "Open Source". Great, great video! Reply @TheTrini1980 5 months ago Thank you for that clear and enthusiastic explanation! Reply @threedot141 5 months ago Oh my, you have provided such a brilliant explanation! Thank you so much! The way you build up the explanation, and also your enthusiasm, is just fantastic. Reply @scorch855 6 months ago As someone with more of a CS background than math or physics, tensors give me strong functional programming/lambda calculus vibes. The higher rank tensors are just like a function which takes two simpler functions as input. It also fits really well within the framework of logic programming. Super cool to finally have an intuitive understanding of tensors. Thanks for the vid! Reply @Hunterfury_44 3 months ago first video of you and im already a fan <3 Reply @yyq90 1 month ago This is actually save my life Reply @som9428 3 months ago I felt so happy learning tensor , i had never seen tensor that way , Make a second video for higher rank teach !!!! Reply @prova5468 1 month ago Fantastic video man ! Reply @octopus-b8y 4 months ago Thanks Mahesh ji it was helpful! Reply @satechknowledge2303 2 months ago You are amazing Mahesh 💗 just don't stop making videos✨✨✨ Reply @cbgee674 2 months ago (edited) Very nicely done. Note the connection with abstract linear algebra -- you have described a linear transformation. :) Reply @misnik1986 2 months ago waiting for a video about rank 4 Riemann tensor Reply @mpperfidy 5 months ago Very interesting video, thanks. Made even better by the fact Feynman addresses you by name! Reply @JamesOmoro-m6m 6 months ago Brilliant presentation. I look forward to your future issues. Reply @williammc5113 5 months ago Wow that was a great video. I would love for you to unpack and tie in rank 4 & 5 Reply @JoaoVictorCavalcanteMiranda 5 months ago Awesome!!! Thank you for your excitement and knowledge!! Reply @DavidCantwell-l9g 4 months ago This video makes great complementary intro to the Daniel A. Fleisch text 'A Student's Guide to Vectors and Tensors' Reply @fredericklehoux7160 2 months ago I sometime wonder why they make definitions that only those who already understand the concept will get. I was vaguely familiar about tensors and just rationalized them is higher dimension vector while missing some of the important facts. This video filled the gaps i had completely. Reply @ДенисЗаика-к7к 5 months ago Very entertaining and excellent explanation. Please do more Reply @athulcarun 3 months ago superb! i loved the explanation! Reply @tommikivimaki 2 months ago Brilliant explanation! Thank you! Reply @garybender3684 1 month ago very good lecture. I learned a lot Reply @kennethcrandall8131 5 months ago Very clear presentation. Now you can make a video on covariant derivatives to really blow our minds! Reply @penguinmonk7661 3 months ago Fascinating, thank you. Reply @leviathanfafner 5 months ago Wish I had this primer before failing my tensor analysis class. Reply @samkendal7615 4 months ago What a brilliant video, thanks so much! You explain so well and intuitively! Keep it up :)) Reply @Curt-f9o 1 month ago GREAT! Love the T shirt! 😊 Reply @jamesbond_007 6 months ago What an absolutely fantastic video! I love how you systematically develop the idea of tensors and show, by example, why rank 2 and beyond are necessary types of tensors!!! You did an absolutely stellar job with this presentation!!! Thank you!!! Reply @drusillawinters212 4 months ago I loved this video. I do not have the education, but I wanted to actually understand tensors and general relativity. You increased my understanding more than 100%. Thank you, so much. Reply @LymonAdd 5 months ago the ability of linear operators to be a value and an action simultaneously is one of the most beautiful and powerful ideas humanity ever had Reply @shashwatneerajshukla3539 5 months ago Sir can you please make a video explaining the magnetic field and magnet field lines... It is probably the most misunderstood topic nowdays... I've met many students who are preparing for exams like JEE advanced but are still unclear about how magnetic field works Reply @thequest369 4 months ago This is the best explanation of tensor. Sure Feynman was a great teacher, but now we got you who keeps his spirit alive. Thank you. Reply 1 reply @david.miskick 5 months ago I've got lost at Ohm's law, but I like your enthusiasm. Reply @reyes4103 3 months ago Bro the way you explained this, I understood better than fractions when I was in high school Reply @christopherchm2050 10 days ago How did you produce the visual animations? Reply @gregorymccoy6797 3 months ago You've removed some of the fog for me. Thank you! Reply @DeminJanu 3 months ago What is the Feynman Lectures book you're reading (or does anyone else here know)? His writing (well, speaking I guess) is really amazing for developing intuition. I've been reading his QED "strange interaction of light a matter" book, and - after decades of photonics research - again realizing I only understood 80% of a topic I thought I knew well! Wonderful explanation, thank you! Yet another math "thing" I used for years during grad school and didn't even realize I never fully understood it. Reply @SwadheenSatyakam 2 months ago please make the next videos on tensors of all kinds not just space time tensors. thank you sir. Reply @evk404 5 months ago Didn't expect to see a video with Keegan-Michael Key explaining a mathematical concept Reply @SwordQuake2 1 month ago 10:57 it's quite simple really 1 Reply @ajkumar6013 5 months ago Good explanation Mahesh....thanks Reply @darthtastic42 6 months ago So, so well presented. And your enthusiasm is infectious. Pacing, everything. Phenomenal vid! Reply @michaelzlprime 5 months ago best lecture on tensors ever. i think one should mention that in machine learning the meaning of tensor is completely different (just a n-dimensional matrix) Reply @darklordhyper 4 months ago Thank you for this video :) -- from a UG Mechanical Engineering student Reply @anatolykatyshev9388 1 month ago Good explanation! But still don't understand difference between Rank 2 tensor and matrix. Reply @swastikbhandari2644 3 months ago amazing explaination !!! 1 Reply @TejoNegro 3 months ago (edited) In the case of the angular momentum, if you choose the axis properly, the inertial tensor would be a diagonal matrix since each momentum component would only change with the angular velocity along that very component. Reply @Alx-h9g 1 month ago Fantastic explanation, thank you Reply @ace_ln6991 3 months ago If you struggle at the first part, its all about perspective. First was decomposing electric field which is why its easy and special case. The second is decomposing current density which gives us two different equation based on conductivity direction. Reply @natsora6466 6 months ago I'm a biophysics graduate student and never understood tensors until now. This is amazing Reply @geochum 2 months ago I’d love to see a bit more rigor next time: tensors aren’t just “matrices that transform,” and clarifying the formal transformation law and covariant/contravariant distinction would make this truly complete. Reply @PierGen 5 months ago This is amazing! Thank you for sharing and for doing such a fantastic job explaining it. Reply @sdutta8 5 months ago I have watched many of your videos and like this one best. Reply @crescentphysics5758 4 months ago Nice one presentation and conceptwise Reply @sciencelover65 6 months ago (edited) Want more and more video on tensor.. Pleeeeeeeese Reply @BrianCombs-xr9op 1 month ago Gotta Love Feynman GOAT my Reed Professor, David Griffiths, used his work to teach - old memories - thanks Reply @CharlesTaylor-t1x 5 months ago (edited) After watching you, I realized that, you can make any niche interesting to watch. "Interesting" meaning,not only am I understanding it, but it doesn't make me feel like I'm receiving lectures, I'm being entertained. Amazing Reply @sfs8730 3 months ago This Is Insanely Good Reply @yocats9974 6 months ago I've had this video in my watch later since it came out and I've seen the title and thumbnail change like eight times so far Reply @SeanBlantonPhD 2 months ago Mahesh, you are one of the best teachers of physics EVER :) Great job! Reply @speakertoanimals 4 months ago This was a great presentation. I appreciate "this is how I understood..." more than "I'm smart, let me teach down." Reply @Masqueey 6 months ago I love your enthusiasm (and your constantly increasing level of energy), thanks for this video! 😊 Reply @ranjansingh9972 3 months ago Outstanding video, simply outstanding. Reply @datkumar1024 6 months ago Perfect YT recommendation after watching the 3Blue1Brown Linear Algebra playlist 1 Reply @NetLinuxAI 1 day ago It's really simple: You know what a scalar is: essentially a number, like a coefficient or offset. You know what a vector is: a 1D group of scalars. You know what a matrix is: a multidimensional group of scalars, usually shown as 2D. The group term for all of these is a tensor: rank 0 = scalar (0D), rank 1 = vector (1D), rank N = matrix (multidimensional). It's just a group of numbers that relate to each other in a structured way. There's nothing more to the term than that. Reply @vasiliynet3425 1 month ago Awesome! Thanks a lot! Reply @hellonepp 1 month ago Mahesh sir, I am waiting 😊for the video on deriving x.P>= nh/4pi from your heisenburg uncertainty video❤ Reply @EnnuiArduous 3 months ago 00:56 well... I do not even need to pretend. 2 Reply @lajosbaranyi7333 2 months ago You are a really good teacher!!! Reply @MCWaffles2003-1 5 months ago Dude... Thank you <3 Reply @Disillusioned_one 5 months ago Oh my god, that was unbelievable. Reply @MrLethalShots 3 months ago Awesome video! Was a little surprised how much you underplayed the coordinate transformation parts though. Maybe a part 2 video on that? Reply 1 reply @aboubacaralaindioubate6086 4 months ago The algebraic definition is so clear...😊. Reply @sivasakthisaravanan4850 5 months ago 11:55 I need 3 heads to think about it 😊 Reply @seanfisher8999 3 months ago It reminds me of biology punnet squares for recessive and dominant traits Reply @kravisha1 6 months ago you have proved that you can learn almost anything by applying observation, thought and common sense. no need for bombastic formulae.. that is what i admire the most in you.. Reply @kaimather7923 6 months ago This is a terrific explanation Reply @Albtraum_TDDC 6 months ago In the end example with how much the space stretches and squeezes in the y direction and the z direction, isn't it the same factor? 1 Reply @bradleybudinger1260 4 months ago Got it... Thanks you!!! Reply @ontogeekchic 2 months ago Perfect explanation Reply @arashshafie5077 4 months ago yes , please explain all that special reletivity used tensors Reply @NathanielAtom 5 months ago In many if not most physical systems that use tensors, there's a symmetry where the yx component is the same as the xy component. So instead of 9 components in 3D conductance would have 6 unique components Reply @physicswithprakash2214 6 months ago Please make videos on Ricci tensor, Curvature tensor, etc. Reply @htchtc203 6 months ago Very good and intuitive presentation. Thank you Sir. And your enthusiasm is really nice and catchy 😊 Reply @gnanaprakash-ravi 4 months ago Great Explanation Reply @sedeheless 6 months ago My dream would be to see your explanation of what the heck means the covariance or the contravariance of a tensor. Reply @oscarbizard2411 3 months ago Thank you Mahesh. Thank you. Reply @YadunandSS 3 months ago Best experience listening to this amazing one Reply @coledavidson5630 5 months ago 18:51 i always wondered how the direction of electric field in a piezo was determined. Never thought it would be this crazy lol Reply @iurk0_streaming 2 months ago Absolutely amazing Reply @jesusgarciarubias6357 1 month ago Great explanation Reply @dailidonistimur6873 4 weeks ago It’s just one way to describe system of coordinates that’s all. You could use angles between the vectors in N dimension and corresponding scalars for each of the axis the result would be the same. Reply @prplplay 5 months ago can you make a video on EM waves? today I was learning about the 3D WPT setup but got really confused. Reply @Avokadik13 2 months ago (edited) 12:10 When you said that one mass is a gravitational charge and one is inertia, I was like oooooh, that’s why. So cool Reply @tuahsakato17 2 months ago Damn Mahes, quality lecture right here, thank you! Reply @ChaineYTXF 4 months ago Thhis was a particularly good video. Rarely do I ever come across one. 👍 Reply @francoislanctot2423 6 months ago Very nice explanation, thank you! Reply @healexhelixvideos4680 5 months ago This makes a lot of sense after having just learned about geometric algebra and the outer product. Reply @devrimyazici4170 3 months ago Since the friction force f and the normal force N act in different directions, the coefficient of friction μ, in the equation f=μN, is also a tensor quantity. Reply @AnshYadav-tf1ni 5 months ago Hello Sir. Can you please make a video on Normal force? I have always been confused in it and what i have felt most of the times is that nobody teaches it correctly or the right way or the complete matter about it. I have presented my query to many teachers but i still couldn't gasp Normal force. Like... What would have happen if there were no normal force? Will the book kept on my table break through it? Or will i get stuck in ground if i stand? Secondly, in examples where a block of mass m is placed on the ground, people show weight mg downwards , then say that the ground exerts a Normal force on the block to counter mg in opposite direction, then again they a second normal force exerted on the ground by the block in response to the normal force applied by ground. But then Sir, how are these three forces balanced? Doesn't the equation come out like -mg+N-N? And that will certainly not be equal to zero. Oh sir please help me. Even the tension force makes me confused sometimes. Thank you so much Sir for your valuable efforts and time. 1 Reply @VicenteCuellar 5 months ago fantastic explanation! Reply @malashukla9292 3 months ago Well explained Reply @SapereAude1490 5 months ago Actually, coming to this after learning about homogeneous coordinates and affine transformations (from graphics programing) makes it trivial to understand. Can't believe I didn't get it before. Reply @TnseWlms 5 months ago I thought it was just a brand of desk lamp. Reply @Berend-ov8of 2 months ago This is one seriously nice dance of insight, leaving ma as an interested viewer with a general sense of having learned something, even with my limited understanding of math or physics. This applies on anything that can be expressed in numbers, and defines linear dynamic of anything that can only be expressed in a multitude of numbers. It allows for the calculation of the off factors of multi dynamic similarities. Etc. Etc. A Very informative video, thank you. Reply @asaflevy9387 5 months ago Great stuff! Thank you Reply @davidh2083 3 months ago Brilliant explanation Reply @alexjaybrady 2 months ago Love love love these vids Reply @Utkarsh-d7i 6 months ago Really love your videos mahesh! pure logical explanations from scratch. can u pls make videos on concepts regarding rotational motion that often confuse students Reply @taleofknowledge 3 months ago Please and please make more videos about them Reply @anvartaziev 1 month ago Я три недели ходил, пытаясь осознать тензор интуитивно, и это видео нашло меня вовремя Reply @sherinsaraphilip1869 6 days ago What do you use to make these illustrations sir Reply @iamtb100 4 months ago Thank you.. learned a lot,. Reply @afifzilani 5 months ago I love your teaching style😊 Reply @enestastan7147 5 months ago I just cannot express the joy I had while watching this video. like, "the pleasure of finding things out" (by Feynman again :)) can be read from all of your uncontrolled reaction of laugh and happiness. That is what the natural sciences are all about. just the pleasure of finding things out about the nature. Even just a simple question can lead to such discoveries. Thank you for sharing this video and your joy with us. Reply @babybalrog 1 month ago excellent explanation!!! Reply @ClarkeWellborn 3 months ago Very good job. Thanks. Reply @TheYogai 5 months ago Been pondering strange ways of life and how strange audience we are. Well, I am. Here, in Cracov, Poland. Late in night. Eating Japanese food. Drinking Japanese beer. Watching Mahesh bringing yet another splendid material and having fun with tensors. Wondering what ppl next table are thinking. Anyway, good job and thanks. Reply @kirilllarin3945 5 months ago Thanks man, I`ve never deal with tensors, only hear about it. But now, when I will need to learn about it, i definitely will have much less trouble with it. (Sorry for bad English :D) Reply @antonmartynenko93 2 months ago awesome! make more simple videos about complex stuff ♥ Reply @LimbLengtheningJourney 2 months ago Damn bro, awesome video!! Reply @rudyyee7453 2 months ago Absolutely great!! Reply @felipegmrqs 5 months ago Tensors acquire another defining property when you work in non euclidean spaces: they need to have a coordinate free description, this property is what makes "tensors transform as tensors" The biggest example of how relevant this property is manifests in the context of General Relativity, where all deformations in spacetime must be described in a coordinate-free fashion. There we have many tensors such as metric tensor (rank 2), Riemann Tensor (rank 4), Weyl Tensor (rank 4), Torsion tensor (rank 3, however this one isn't necessarily relevant in most formalisms) Reply @abubakarralieubah5398 1 month ago you've saved a brother!! Reply @Ἀντήνωρ 5 months ago Best video on the subject i have ever seen. 😀 Reply @lucaskohn5457 4 months ago (edited) I understood it during a mechanics class about rotation where tensors are also applied. I don't know however what would a higher rank tensor mean Reply @joehutter7083 5 months ago Great explanation Reply @pizzablender 5 months ago Excellent explanation. Only thing that distracted me is our face sometimes being hidden by the black microphone. Reply @Chowe1367 4 weeks ago Great video.Very easy to understand . I would like to learn all this deeply but to do a phd one need good marks which I don't😢 . Reply @IW2MXP 2 months ago (edited) You are a great teacher. Thank you for this nice lesson. It could be extended to cover eigenvalues and eigenvectors using the same examples you gave..😉 Reply @ruchir2 2 months ago One of the best science channel on YouTube. Hidden gem. I just love @Mahesh_Shenoy's enthusiasm and ability to break down complex topics into simple language for everyone to understand. I wish this is how science and math would be taught in school. This will make kids want to pursue science much more. Reply @NinjaS006 2 months ago The same with stress analysis in materials :) Reply @pschalkx 3 months ago Hello! I really liked the fluid graphics, and I need to make some for a project. What did you use to make them? Reply @arv2ms 4 months ago Journey from tensor to grasp the concept of block Universe and noether theory Reply @thelifeexamined 6 months ago As you taught, I kept thinking are we missing some computational efficiency by requiring 4 numbers instead of acknowledging the coordinate transformation where introducing one angle, Theta to describe the rotation of the relative coordinate system uniquely defines the 4 numbers in the constant for a rank 2 tensor with just 3 numbers. What other ramifications are there? Big O notation and Mohrs circle comes to mind as intuitively related. Thanks for the systematic and enthusiastic explanation! Reply @jgir100 6 days ago (edited) Mahesh, I very much enjoyed your elucidation of Feynman's explanation of tensors. What is confusing me is Einstein's use of the rank2 tensor where the variables are mu and nu. Drawing from your (Feynman's) explanation, the tensor should be summing the proportionality constants of nu with respect to mu. I am not able to find however a good definition of what properties these two variables represent. The closest that I have found is that they are "spacial or free indices", which is not satisfying. Can you shed some light on what two properties Einstein was representing in mu and nu? To keep it simple, I would be happy if you would limit the explanation to just the left hand portion of his GR equation relative to spacetime curvature. Reply @victorarnault 5 months ago Thank you for this explanation! ❤😊 Reply @pmariner65video 6 months ago You're one hell of a genius! I studied tensors at physics university, but I didn't understand a damn thing... Thanks a lot Reply @GeorgeN-Tbilisi 2 months ago Great explanation... thx Reply @ЮрийАндрейцев-й1з 4 months ago lets go for 500k subscriptions Reply @gustavoexel5569 4 months ago I like visualizing rank 2 tensors as ellipsoids, with principal axis aligned with the eigenvectors, and radii proportional to the eigenvalues. That way the 9 components are less arbitrary, and so are rotations and coordinate transformations. Reply @nirmalrajeev4237 6 months ago You definitely gained another follower. I wish I could've found you before. Keep it my man! Reply @abdelkrimrachedi5922 5 months ago Beautiful .. Thank you Reply @badatpseudoscience 2 months ago Fantastic video! Just subscribed and liked. Reply @GyovanneMatuchaki 5 months ago Congratulations! Fantastic content! Reply @harvesterharvester 1 month ago Thank you ! Reply @markonar140 6 months ago A Very Cool Creative Inspiring Video!!! Thanks for Sharing!!! 👍😎✨️ 1 Reply @Robinson-1878 6 months ago You make math fun, this would be dull and totally fall flat any other way. Happy you exist Reply @arv2ms 4 months ago Great Explained very well Reply @i77777 1 month ago Hey Man, nice video! Would you cover 4th order stiffness tensor from Continuum Mechanics? Thanks! Reply @jet3xi 5 days ago so LLMs are just N^X tensors with X a very large number. Reply @AnweshaKatuwal 2 months ago We need more about tensors Mahesh, I just found my first love Reply @ishandhar2851 1 month ago Love you man Reply @kavinyudhitia 4 months ago Beautiful! Reply @PhotonDynamics 6 months ago more videos on tensors &how it apperar in relativity Reply @JackAdrianZappa 6 months ago Great vid! Ty! Reply @custominvest1270 2 months ago This is the best video ever Reply @Khushdev-k3o 1 month ago ❤ Explanation level 💯 Reply @MafistoPL 5 months ago Brilliant video Reply @Genie0007 5 months ago Great explanation 🎉 Reply @kephalopod3054 6 months ago Wonderful video. Reply @amaljeevk8903 5 months ago ❤ we need further videos about tensors❤ Reply @rrshier 2 months ago That is exactly a rotation matrix! Reply @tamfang 5 months ago I have The Feynman Lectures but have never opened it. Guess I'll look up the tensor chapter. Reply @Tony-m5t 3 months ago Well done. Reply @robinxavier1494 4 months ago thanks brother. Beautiful Reply @coveringjapan 14 hours ago I like magnitudes 😮 Reply @MrFaalke 5 months ago amazing broooo ❤ Reply @davidjsutherland 5 months ago Good video. Thanks. Reply @varaprasad5559 6 months ago Where to study this (source of video ) 🙏🙏🙏 Reply @Slowensko98 5 months ago now - at the end of my study - i understand, thank u! Reply @Shua.a 6 months ago I LOVE YOU VIDS SO MUCHH you helped me love physics again, I wish i had my whole book explained by you, how do i understand this more than the simplest highschool concepts😭🙏 could you explain or do a video why dot product gives scalars, but cross product gives vectors? Reply @Hötzendork 6 months ago I would love a video on contravariant vs covariant tensors. Mathematically, they're fine, but again the intuition could use some help. Reply @ahmadgnizam72 2 months ago Very nice man Reply @Ruzsu1_1 1 month ago best physics channel Reply @DigiBentoBox 5 months ago This video was truly beautiful. I know you give Feynman a lot of credit, but sir, take a bow yourself, you make us feel so welcome, and so invited to the conversation of physics that you inspire LOVE of learning. That is the highest rank tensor anyone can achieve ❤️ Reply @user-dn7vd7ys8v 6 months ago Excellent video, keep up the good work. Reply @kimjustinelabansawan1005 3 months ago thanks now i can know how to manipulate numpy better Reply @Ketsen 5 months ago I'm shocked it's so cool Reply @jamescyriacajith 5 months ago My question for the last 15 years answered in 23:24 minutes, hope my 'Continuum Mechanics' professor explained it like this! Reply @soumyadeepsaha2679 5 months ago ABSOLUTELY BEAUTIFUL. Take a bow. Reply @tone618 4 months ago I am going out on a limb here when I say this but intuitively I would imagine this is why when one flips say for example a tennis racket it does not just rotate about the axis around which force is imparted. If it starts in your hand flat parallel to the ground the imaginary line cutting through its handle is the x axis. the one parallel to the handle is the y axis and of course z is orthogonal to the other two. the imparted force is around the x axis but because the vector for angular velocity and angular momentum are not aligned despite being proportional the tennis racket will also rotate around the y axis. Reply @FPMwitty 3 months ago Thank you this is amazing❤ Reply @adixit5 2 months ago Tensors represent the quantities which have magnitude and varying direction. Vectors have magnitude and fixed direction. If direction variation is fixed, its rank 2 tensors. If direction variations is changing in two possible positions, its rank is rank 3 tensor. If direction variations take place in n-1 positions, its rank is rank n tensor. Reply @kylebooth2528 2 months ago I'm realizing that a 3d projection matrix is a tensor. I don't know why nobody explains it like that but it's actually helping me understand it better. Reply @Neil-p7q 6 months ago Brilliantly explained, but one thing I don't understand: you gave examples of an equation with two rank-2 tensors and said that the coefficient must therefore be a rank-4 tensor, but with F=ma, shouldn't m be a rank-2 tensor by the same argument? Reply @GurnBograt1986 4 months ago (edited) I am studying AI and AI uses tensor flow which I didn't understand until watching this Physics conductivity tensor explanation. Thank you!! I just subscribed!! Reply @s4ulyaniv35 5 months ago Excellent explaination! Reply @zachos-un6py 4 months ago I've always just been given the explanation that a tensor is something that transforms like a tensor Reply @EduardoGonzalezCervantes 5 months ago What a great video my brother 🔥 Reply @aashsyed1277 5 months ago I would also like if you made a video which is exactly like this one but it does it mathematically instead of using physics. Reply @robblerouser5657 5 months ago Where were you when I was taking physics!?! Reply @Turbohh 6 months ago fascinating and well done! Thank you. Reply @Paul-jp8zz 4 months ago This was fantastic! I know this is a physics channel, but this tensor concept now goes beyond Feynmann and physics of the "real world" you've described. The large language models and neural networks driving ChatGPT (etc) and their inner workings are all about creating multi-dimensional hyper-spaces of vectors - each vector describing one of millions of words, concepts & ideas (as opposed to just physical properties) and together forming an N dimension concept embedding space, so to speak. Tensors are the data-structures used to describe (and do parallel computation on) all the matrice's involved. Reply @fhtagnfhtagn 5 months ago Idea for the next video: I never understood why electroweak interaction unifies electromagnetism and weak nuclear force. Or, alternatively, I never understood why W bosons has mass. Reply @anweshpaital9157 5 months ago wow this is really good content learned a lot ! 😊 Reply @uvtube2008 5 months ago (edited) There can be much simpler (intuitive to the beginners) to explain the domain of tensors. An RGB video display is an example. I often quote: 'even a delicious 'sambar' is a "tensor of taste" or an olfacto-gustatory sensational vector complex. And in the case of conductivity function in an anisotropic medium with temporal changes, you could add more axes, or say dimensions, like time, temperature, lattice transformations and so on...) Reply @alice20001 4 months ago OF COURSE WE WANT A DEEPER DIVE! You can't just leave us with a cliff hanger like this! <3 Reply @judethedude7704 2 months ago i have a question with stress and strain its like npow 4 tensor right........... so are ;y;ou inferring there are 2 output forces ... which is not possible because we take the force in space as one and it has 3 components but its a single force 1 Reply @FL-rk1pb 5 months ago Well, thanks... in 30 years of trying to figure out intuitively what tensors were like, this is the first time I really managed to wrap my head around :) !! Now, we'd need to deal with co/contravariant coordinates .... Reply 1 reply @crazypyrokitty 5 months ago 6:40 is exactly why everything is relative. Measurements are distorted by the intrinsic perspective of the observer. Reply @not_popskgaming8150 6 months ago (edited) 15:23 booooom. Clear as day example about tensors as I varies across which axis you spin it about. Wow great video . Reply @TheFarmanimalfriend 5 months ago It appears to me, for a 3D object, you will necessarily need rank 3 tensors and if you add time - rank 4 tensors. Reply @macpr0c 3 months ago That is not all a tensor is, what you are showing is a special case of tensors. In physics (excluding general relativity studies) and engineering tensors are usually applied as multidimensional arrays/matrices, as you do in this video. But by itself it is not apparent or computationally emergent that they are independent of coordinate basis. The true might and identity of tensors become apparent in advanced mathematics classes like DIFFERENTIAL GEOMETRY which you use tensors to calculate transformation between manifolds and tangent spaces. In such research areas, you consider tensors to be multilinear maps. And they become even more mind boggling but amazing in the process. I took that class and I'm still not intuitively sure what a tensor (in its entirety) is. 1 Reply @5_inchc594 2 months ago pure gold Reply @erockbrox8484 6 months ago That t-shirt fits the channel perfectly, however just a regular shirt would have been just fine. Reply @dng88 2 months ago (edited) A great video on explaining rank number and how it comes about … but not about tensor itself. Tensor is trying to find a way to describe a physical object which should be the same across change of coordinate system. special relativity where coordinate change need tensor as it want to find the invariant due to the subject coordinate system is different. For the excellent example at 11:19 those number are needed because we change coordinate system. And the great moment of revelation of n^[tensor rank] is only the beginning as what happens not just adding dimension but has two different observers using two different coordinates relative to themselves and travel relative to each other (constant and if accelerate then rotate as well). We need something that is invariant. Just n-dim ^tensor rank is not enough like 19:12. We need to find a relationship that stays unchanged. Or invariant of these numbers. That search for the invariant is the search of the tensor here. Not just the rank and its number. Reply @ollieoniel 4 months ago You would make a great teacher. Reply @rizkiaprita 6 months ago i love this particular video. Reply @ianlaughlin85 1 month ago (edited) I remember taking linear algebra and trying to wrap my head around higher dimensions. Our brains just aren't built for it. In robotics we use coordinate transformations to relate the end effector to it's position in real space. You absolutely need a computer for these types of calculations. It would take centuries to do simple program calculations by hand. Reply @GufranGuest 3 months ago omg i love ur video, the exitement ❤ Reply @enzoaugusto8278 3 months ago Hi! I would like to ask what do you use for the animations, especially the ones from the start of the video. Reply @imusthafaajawid1915 5 months ago I love the T-shirt 1 Reply @lolcat69 6 months ago so it's like in game engines, where you use "transformation" matrices to move around vertices in the 3d world, like the projection matrix, translation matrix, etc... makes sense! Reply @SingingWraith98 6 months ago Yes make videos on Reimann and Ricci. Reply @Sheokand.sourabh 5 months ago i have a master degree in physics but i never see that much details video about the tensor and how they work this is very very good Reply @robcarnaroli269 2 months ago So gotta ask, the thing where an object in space will spin for a few and then suddenly flip the other way and spin some more, is that because there are some force vectors acting on it that we don't assume in a cartesean model? Reply @ruslansergeev4061 2 months ago You have a serious talent 😂🎉 Reply @devang1304 5 months ago 14:49 if they are in the same direction, why would it be scalar? Shouldn’t it be a vector?? Please clarify. Thanks! 1 Reply @omaralhafez5014 5 months ago You are great man ❤ Reply @qandak 2 months ago 20:39 "You can think of Tensor as a machine. A machine that takes in one vector or a tensor and outputs another vector or a tensor." It's a recursive definition and similar to the definition of higher-order function, that - lets's say - "takes in values or functions and outputs values or functions". Reply @andreaswiklund7197 5 months ago Awesome! Feynman would be proud of you. Reply @dasprakash2753 1 month ago I would like to understand how eigenvector and tensor are connected Reply @kephalopod3054 6 months ago You were lucky at the beginning because the coordinates were aligned with the eigenvectors (output vector is eingenvalue times input vector) of the matrix. With a rank 4 tensor, mapping a rank 2 tensor to a rank 2 tensor, do you have such a thing as a rank 2 eigentensor such that the output is a scalar times the input? Reply @MarkMurk-tv7br 1 month ago good stuff Reply @kho2333 6 months ago 19:11 you dude I heard you like tensors, so I put a tensor INSIDE your tensor! 😂 (for real though, love the enthusiasm) Reply @Inzomniac9 4 months ago good stuff thanks Reply @MrRiVoS 6 months ago Man, amazing video!!! Reply @treyweaver5396 5 months ago Good vid! Reply @NickKeighley 1 month ago I never found them particularly mysterious Reply @UziBiton 5 months ago Thanks. That was interesting and beautifully explained.. you are great Reply @CarlosHenrique-er7zq 5 months ago Wow, mind blowing Reply @techie1143 4 months ago The surface of tensors best scratched😅 Reply @awnf82 3 months ago In the example, why would the elements of the matrix vary across rows? Shouldn’t the conductivity be the same in a direction regardless of which component of E it’s coming from? Reply @joemarz2264 11 days ago My Pixel 10 has a 5-th rank Tensor (Tensor G5) 😄 Reply @TheVigilancer 5 months ago where is link or at least name of the original paper? Reply @petevenuti7355 6 months ago When you said figure it out yourself I'm thinking figure it out from what Reply @dayaalex8693 5 months ago Fantastic! Reply @YodaWhat 5 months ago Very good! Reply @chiamatthew6829 1 month ago Any example of what would have been tensors except that the relationship between the 2 object tensors are not linear? How about a stress tensor for a non-newtonian fluid? Reply @eltonhuang329 2 months ago I thank you for bring this to me but can’t really deal with the emotional presentation. I’m going for his writing. Reply @bodypilot2006 5 months ago That was fun Reply @peters972 3 months ago I felt less tense after this video. Reply @VicenteCuellar 5 months ago more videos yes! Reply @Kaiju3301 6 months ago Tensor calculus pissed me off but I’ll still watch the video. Reply @xeoncat 4 months ago Amazing talk, thank you. I assume the rotational MI is used in gyroscopes Reply @gjoe3756 5 months ago Good vibes and high energy. I like it Reply @IBankRunner 3 months ago Tell me if I'm missing something, but tensors seem like just a way for physicists to make their equations look elegant when really they're not, because if you look at a simple equation with tensors in it you can't just plug in numbers to get a result. There's a lot of other stuff you have to understand to know how the tensor operates. 1 Reply 3 replies @vikashvarun123 6 months ago Hey Mahesh, Why dont you make a video on antimatter and hypernucleus Reply @itsahexagon 5 months ago so... conductivity has eigenvectors, right? they're the special cases that we "got lucky" with on the example crystal, the specific directions in which J is the same direction as E just scaled by a scalar. rephrasing with tensors... a rank-2 tensor has eigen[rank-1 tensor]s. does this imply that a rank-3 tensor can have eigen[rank-2 tensor]s??? Reply @ArmandGilbert 5 months ago This was great. Reply @Rossomow 3 months ago I still can't get through how a vector equality may mean different directions. Like........that is WRONG. THEY MUST ALIGN or if not then the equation doesnt make sense 1 Reply @MedievalSchneefuchs 3 months ago Thank you soooo much for your damn cool videos! Greetings from Germany! Reply @refusneant 3 months ago perfect .You are the best❤ Reply @johndoyle2347 6 months ago The square root of (e + 1/e) divided by (e, cubed), is the constant of integration for the speed of light, and is the basis for our hindsight abilities. It helps explain time dilations. From comparing the mathematics when dropping the base from Doyle's constant to ignore strong force considerations and dimensionally expand the weak force, so as to understand the elliptical mathematics (SSA), viewed from polar equations of trisectrices. I have talked about mathematically proving the Riemann hypothesis in terms of Big Bounce physics. I talked about using absolute values to treat complex numbers like a 1, adding to the 1 of split-complex numbers to understand the amplification of gravitational aspects of singularities to get to 2nd degree dual numbers contact - almost like stacked pancakes. When black holes are broken in a Big Crunch, leaving mediants, you lose all stability considerations in three spatial dimensions and effectively go back to negative 1 with the formation of dark matter. This constant of integration was what I was using. By multiplying the constant of integration for the speed of light to my CMBR equation, I am able to see inside the bonds of atomic nuclei: (e, squared + 1), squared, divided by e to the 6th power, divided by e to the (e + 1/e) power, and divided by (e to the i times θ power + 1/e to the i times θ power). (e to the 6th power is an important limit of spacetime for particle stability.) "e to the 9th power": from a further multiplication of the constant of integration for the speed of light, for a second derivative. This mathematics gets into thicker singularities being allowed in superheterodyned photons and in aromatic resonance. The Delanges sectrix "demands" a pairing or ellipse of some sort, here. Surface tension also relates. Using your closed thumb and index finger to overcome nearsightedness gets into this mathematics, with a virtual image duality and an amplification of the weak force creating a lensing effect. Note: (e, cubed) times (pi to the 4th power + pi to the 5th power) = e to the 9th power, reminiscent of a Pythagorean triple. "e to the 12th power": from yet another multiplication of the constant of integration for the speed of light, for a third derivative. This mathematics gets into the end of laminar flow for the Inflationary Epoch, blood flow between systolic and diastolic pressures, and relates to the Dinostratus quadratrix. It is the limit of angular momentum and tilting angle before dark matter is forced to break from impact. Reply 1 reply @louismartin4446 5 months ago My Tensor is a bandage and it wraps around my head in many directions! Reply @alice20001 4 months ago For some other video. I would love to see examples of Machine Learning. Images are an example of rank 4 tensor and video rank 5! Because, although they do not follow the more mathematically strict definition of "a multilinear map between vector spaces" and more towards a N-Dimensioninal Array. These "close to home" examples and analogies really helps me "intuitively" ;) understand some definitions and could be a nice stepping stone! What do you think chat? I would love to hear your opinions! Reply @kawaiikaktus465 5 months ago My physics knowledge is absolutely limited because i always had bad theachers and i never got the right entry due to adhd but if my professor at uninwouldve explained stuff like you did i wouldnt have switched to economics 😂 i love this video Reply @patrickfox-roberts7528 6 months ago The stress strain case is much more intuitive to me because direct strain, shear strain and poison ratio etc all easily, physically visualised. Reply @adeebh.s1915 5 months ago I'm so glad I tapped on this video!!! Reply @Pedritox0953 5 months ago Great video! Peace out Reply @wenlamboMMD 5 months ago i feel like is probably some assembly code data structure in the pytorch. Reply @bhaskarsingh3901 6 days ago What about E=mC²?what Rank Tensor it has? Reply @kirbymoore7603 4 months ago Excellent!!! Reply @crabcrab2024 3 days ago 19:00 to 19:20 is absolutely unclear. I completely missed the reasoning. Could someone explain, please? Reply @SysFan808 5 months ago 5:40 my current thoughts are that the conductance itself has to be a direction. Reply @tarkesdora20 5 months ago the advanced topics wold be great Reply @MH-sf6jz 5 months ago Tensor is not hard to understand, it’s just a kind product that has behaves like multiplication of real or complex numbers in the sense that scalar can be pulled out from each entries, and one can pull out sum from one entry while keeping other entries fixed, which is mimicking the distributive rule for real multiplication. This is different from the Cartesian product because the scalar multiplication distributes to all entries instead of one, and sum can be pulled out without the need of keeping other entries fixed. The real problem is to show why the physical nature of some object is well-described by the tensor product. Reply @UVB4U 5 months ago Love your enthusiasm, great explanation! I'm fully subscribe Reply @skeleton_craftGaming 6 months ago I never realized that coordinates was co-ordinates... Reply @Dickelul 6 months ago WOW, what an energy U got! ❤ (I think I understood most of it. I'll have to watch it again, maybe.🤣) Reply @saurabhnaik430 5 months ago Thanks for such an intuitive explanation. If rank 2 matrix is 3x3 matrix then does rank4 tensor is a 3x3x3x3 matrix? And then how the matrix multiplication rules apply? Reply @AyushSingh-be2nm 6 months ago Bhaiya! Just cover all of the contents of Feynmen Lectures at least Vol 1 and 2. Reply @kiryllshynharow9058 5 months ago Amazing! Reply @shreyalmaloo9090 1 month ago (edited) The t shirt is superb.Flux being 0 in the cube,;what a nice pun.Also yes continue this series for higher order tensors Reply @2s_company_ 7 days ago pardon me, I'm a dud why do we only consider the spatial direction of the flow in the crystal to determine conductivity? why not temperature? Reply @JohnMichael-h8z 5 months ago I don't see how 10:06 was such a huge discovery, it was kinda obvious from the start, but I love his enthusiasm, it's infectious. Keep up the good work, love your teaching bro Reply 2 replies @andreiso9624 5 months ago Okay, I need someone who could go a bit more into detail here, 9:21. In my mind I see the component E_x as the projected vector of E onto the x axis, the same goes for J_x and J_y with respect to J. Therefore, in order to express J_x in terms of E_x, we would only need one number, sigma_xx in this case, because these vectors lie in the same direction. On the other hand, J_y and E_x lie on two completely different axes, and as such we would need a rotational matrix in order to express one in terms of the other, in this case a 2x2 matrix, so it would be 4 numbers plus the one we got from expressing J_x in terms of E_x. This is obviously wrong as we could simply apply a rotational matrix in the first place and get J in terms of E. I know I am missing something here, but I can't figure out what exactly. If anyone is willing and able to help, I would appreciate it a lot. Reply @OVERLORD-ji2id 6 months ago Perfect energy Reply @christophmatthews5889 5 months ago Great Video Reply @x_ma_ryu_x 4 months ago Thank you Reply @yogiHalim 5 months ago Thank you Reply @KimberlyRPeacock 4 months ago ❤ I love your mind. Thank you. I love this and your channel. You are like a party for my mind. Reply @SangamRane 4 months ago Hats off ❤ Reply @DanielDogeanu 4 months ago If more people had the enthusiasm you have for math and physics, the world would be a totally different place! Reply @SnowBol8991 6 months ago I have barely seen a man this happy before 💙 Reply @AbhishekTripathi-o1j 5 months ago Love the inverted hand clapping repeatedly to make me notice the moment - rank 2 tensor! I almost said is in chorus. 😂 Reply @JonathanMandrake 6 months ago What took me a while to ignore is my intuition regarding how matrices multiply (which is why it was obvious 4 numbers were needed) Reply @gilber78 7 days ago My status on discord for nearly 6 years now has been “what the f*ck is a tensor” Reply @saiprasadrakasi8442 5 months ago thank you Reply @Ubiquities 2 months ago 1:00 no problem, I got this Reply @dhcmega 6 months ago Can you please enable the auto dubbing? Thanks!! Reply @dalriada 6 months ago Stress and strain also make me tenser. Reply @aajas 3 months ago There are 2 types of friction— static and dynamic— and they each have a constant. I know because I read it in a book Reply @Raptorman0909 2 months ago Basic FloatHeadPhysics approach to a video title -- ALWAYS SAY YOU NEVER UNDERSTOOD #$%#%$# UNTIL NOW. Go back over FloatHeadPhysics videos over the years and this approach appears over and over and over and over and over and over again! Reply @santerisatama5409 6 months ago Thank you! The relative conductivity of directions give me sufficient computational intuition for what the fuss about tensors have been behind the obfuscation of coordinate systems and numerical metrics. Conductivity is relational to various qualia of complexity, and thus sense analogous to the Big-O of computation science, which is an empirical heuristic in a rather limited context, not a fundamental theory. Now I can locate the basic intuition of tensors in the coordinate independent construction originating from my interest in foundations. Which is the following algorithm of concatenating mediants from the minimal operator language alphabet consiting of < and > which already notationally give iconic mirror symmetries of reversible computing. < > < <> > < <<> <> <>> > etc. Tally in each generated word <> as the denominator element and < and > which are not part of <> as the numerator elements for Stern-Brocot (SB) type top-down number theory. "Irrational numbers" are here non-terminating zig-zag paths of continued fractions along the binary tree of blanks between the words. The L and R directions of zig-zag paths can be written as < and > for notational parsimony and intuitively synthetic further investigation. The alphabet < and > symbolized continuous directed movement (Cf. Catogory theory simplified to arrows only and vectors unbound from their coordinate system prison). Which is more conductive, reading/writing the mirror symmmetric rows (Cf. Turing Tape) or the diagonal binary tree paths, is perspectival and depends on the various syntaxes derived from and applied to this metric as well as the computational substratum (machine/mental/etc), so this opens a way to study and develop a "type theory of tensors" starting from the elementary operations of concatenation, whitespace and copy-paste generating and organizing the ontologically primitive constructive operators < and >. Rotations come in this picture from simple bidirectional bit rotation between strings <> and ><,which are also Boolean inverses of each other. Mirror symmetrically reversible substrings of the same loop share thus doubly reversible property with each other. As it happens, the string lengths of the row-by-row SB-type construct presented, blanks included, follow the hyperbolic pattern 1^n+2^n+3^n, which can be seen as a kind of superposition inverse of the topological dimension perspective scalars->vectors->rank2 tensors. Or that the latter trinity has a logarithmic relation with the former. Mereologically aka information theoretically topological dimensions are nested in fractal dimensions. Dirac showed with his comb how to translate between those. Reply @peterweston6588 5 months ago Thank you. Reply @akash_mechanical 6 months ago (edited) For a better experiencing a tensor, one can do a small experiment. Take a L-shape object. Bend your steel spoon (just kidding), now apply torque or rotate by holding one of the end and release it in air. You will notice it will change the direction of rotation. It says, the direction in which you have applied torque and the direction inwhich it started it to rotate in free fall are not same, it will not rotate in same direction. It is similar the satellite example explained in this video. One more task , please took into the inertia tensor of a cube {it is diagonal}, and then look into the Inertia tensor of a L- shaped object (like a bend steel rod), this has off-diagonall terms too. 1 Reply @2.99e8 4 months ago The Feynman lecture textbooks are THE BEST investment I’ve ever made lucky enough to have gotten a nice 25th anniversary edition his explanations are absolute cinema Reply @clivehazell2790 1 month ago Has anybody ever thought of the psychological correlates of this? Reply @AjitSharma-km6ev 4 months ago At 19:12 you said for piezoelectric effect formula E = pS, (n1) = [p](n2), so [p] must be rank 3 tensor. Not convinced yet. E is a vector represented by n numbers so lets call it (n), S has n*n values so it would be (n^2). If we apply matrix multiplication (1 X n) = (1 X n)*(n X n), but this gives p to be degee-1 tensor and not degree 2? What am I missing here? Reply @fixed-point 5 months ago The Rank 3 and Rank 4 examples have a logical hole. You don't make any mention of inner products or outer products. In the rank 3 case, for example, without knowing whether the vector is a row vector or a column vector (in matrix representation) we don't know whether the piezo quantity ought to be rank 3 or rank 1. In other words, we don't a priori know just from what you have shown whether we would be summing over indices. Imagine on the right-hand side there were 2 rank-2 tensors, and a mystery quantity on the left. Well, if you think of the rank-2 tensors as matrices, your intuition would suggest that the quanity on the left-hand side is also a matrix, because that is how we define matrix multiplication. But if we were to apply the intuition you were using at the end of this video we would think the left-hand side would need to be rank-4, which doesn't even make sense to someone only familiar with undergrad linear algebra. But really in the case I just gave the left-hand side could be rank-0, rank-2 or rank-4 depending on how indices match up. 1 Reply @juandavidmitrecedeno6890 6 months ago I love your videos. You really transmit a passion and joy for learning that I enjoy and share with you 🙏🏽 Reply @ukkomies100 1 month ago I try to understand moments of inertia tensor in my dynamics courses and the indices always keep throwing off my intuition. Reply @peres9559 5 months ago Yes that clicked in my head Reply @SrChengLX 1 month ago WOW SUPER NICE VIDEO I MEAN I DID NOT KNOW ANYTHING AND I NOW SEE WHAT THEY REALLY ARE NEW SUB !!!! Reply @warriorofislam2529 2 months ago superb Reply @wormjuice7772 5 months ago So its always the amount of axis times the direction vector's you want to know about. Reply @MST339 3 months ago Thanks for the lecture. I have nothing to return so I just let the ads play to their ends 🙂 Reply @dalvirsingh2381 4 months ago damn damn good explanation Reply @nabarunghoshal560 4 months ago (edited) Thank you Mahesh for making this wonderful video for dummies like me. What occurs to me now is that all mathematical calculations should be done in the light of a rank 2 tensor because in nature, no object is a two dimensional one. It is at least three dimensional. Hence, any calculations, if we want it to be correct to the maximum extent, must be done keeping in mind of the three dimensions. However, for our daily life, scalars and vectors will do. Reply @AstonishedByTheLackOfCake 5 months ago loved the explanation, but I don't quite see the difference between a tensor and a matrix unless matrices are just more general containers and tensors are when they encode this specific type of data (after all, a single number could also be seen as a 1x1 matrix, and a vector as a 1xn matrix) so all tensors can be expressed as matrices, but all matrices aren't necessarily tensors? Reply @joelmet1 5 months ago Your explanation is great in terms of conductivity. A question about the angular momentum/velocity example. My intuitive understanding of the requirement of an n2 tensor in a system of equations is that the x component of one variable is dependent on (or creates) both an x and y component in the other variable: this means that the transformation variable (conductivity or inertia - in your examples) requires values for the resulting x and y vectors (current or angular velocity) from the x component of the first variable (electric field or angular momentum). My question is this: for your angular momentum/velocity example, I do not see a case where an angular momentum in the x direction could be resultant from an angular velocity in the y direction - am I thinking about this correctly? And if so, would the angular momentum example only require an n1 tensor (or a vector) for the inertia input instead on an n2 tensor? Reply @oakinger 1 day ago time to undust my feyman lectures and actually read them Reply @StarBoy-t7e 3 months ago Sponsoring brilliant shows how good you was because they dont choose just random Unintuitive teachers who focus on marks, they only choose some great peoples like veritasium, wrath of maths, three blue one brown and you. ❤❤ Reply @MrCreeper20k 5 months ago For the elasticity constant, couldn't the proportionality constant also be a scalar if we're only looking to keep the the rank of the LHS the same as the rank of the RHS? So both a Rank 0 and Rank 4 tensor satisfy the equation. Is Rank 0 just a special case? Reply @Grasshoppa065 6 months ago 10:45 to be fair, you do not NEED 4 numbers. You could use sigma_x , sigma_y, and theta ( angle between field vector and eigenvector of conductivity field) which is only 3 numbers. Reply FloatHeadPhysics · 1 reply @CyrusMohseni-v8e 3 months ago (edited) Thank you Mahesh. Let's reiterate what Mahesh is saying. Tensors are real properties like Vectors. When you exert a force on an object, it behaves differently depending on how you change the magnitude AND/OR direction of the force. So both magnitude and direction are necessary before working out how the object reacts. To explain how objects deform under force we need to quantify 3 values on every point within the object. 1-The magnitude of the force, 2-the surface the force is acting on and 3-the direction the force is acting on that particular surface. If the force is going in or out of the surface it has Tensile effect which has the effect of elongating or shrinking the material. If the force is lying on the surface it has an absolutely different effect. It wants to deform the material by shearing it (like cutting it) that's why it's called shear stress. So Tensors, like Vectors are real beings in the universe and are not just mathematical convenience because, they define an indispensable bundle of separate quantities corresponding to separate effects that are NECESSARY to explain the behaviour of a single particular event in the world. They are an inherent and integral part of any physical property. Reply @SpaceGuy-vw3wb 2 weeks ago ARE YOU THE same guy from kHAN academy videos ? 1 Reply FloatHeadPhysics · 1 reply @hurricane31415 4 months ago The part where I don't follow is that for me, the "yellow" rotation at 7:17 is equivalent to a "green" opposite rotation. That being said I intuitively understand the 2x2 matrix and it make me suspect I don't actually understand anything. I'll have to think about this again after a good night sleep. Reply @nishensemble 1 month ago I love this guy because he also looks like Key from Key and Peele doing an helpful indian guy tutorial. Reply @tobeyh6878 6 months ago Moment of inertia tensor to me is a more intuitive version of this! Electric field is abstract, I can't touch it. I can try to flip my phone and see it spinning weird, that is your off diagonal tensor terms. Reply @gregreilly326 1 month ago (edited) Hi Mahesh. I've used scalars, vectors, and matrices, but not tensors of higher dimensions than two. Thanks for showing us examples of that but I'd like to see the actual equations and the algebra and I'd really like to know if the algebra is similar to 2d matrix algebra. I'd also like to know if there's always a tensor algebra that's similar to 2D matrix algebra for any number of dimensions. Reply @psargaco 4 months ago So, is this Feynman in the room with us now? I'm kidding, dude, excellent video, congrats. Reply @idenityxunknown1656 5 months ago there is one thing i dont understand during the rotating the co-ordinate axes, before the rotation when the E is not align with the x-axis it was named E but after the rotation, when the E is align with the x-axis, the E become E sub x, my question is, is the E sub x == to the E(before rotation), or is the E sub x is another E that got decompose hence made E sub x (align with the x-axis) and E sub y (align with the y-axis) and nother question is , when calculate the E sub y , why did the J shifted to the back if these are just basic math let me know Reply @j69chevelle 5 months ago Why are vectors used in orbital prediction models versus tensors? Would tensors require significantly greater computing power? Reply @anfarahat 1 month ago My only problem with that explanation is that it is coordinate-dependent. Reply @anonymous-4824 6 months ago I can't understand the part where you tell J(x) is contributing to E(y). Both lie on different axis and how could they be equalled Reply @vijaysoman6268 3 months ago Any good book which explains Tensor fundamentals and tensor calculus in a very simple way. Reply @BeiZhang-q3n 5 months ago To summarize, tensors are linear functionals of vectors and covectors. Reply @dib.indian 1 month ago 12:10 TO 12:18 love it Reply @kmagnussen1052 3 months ago What about the inductive and capacitance reactants in the conductor? Reply @cosmm_fly 6 months ago I made tensors at fluid mechanics. Viscosity tensors. Also scalars, vectors, and matrices are basically tensors. Reply @achrafchoiuakh7107 2 months ago boom my head is bowling Reply @Rooftopaccessorizer 4 months ago i got lost early on, so i still dont know what a tensor is. however i love the enthusiasm, and i think i get why hes excited, just not the math. Reply @shyama5612 6 months ago Feynman says 'Mahesh, Good job homie' Reply @doveophesao87 6 months ago Big fan Sir.👌 Can you please do one episode about logarithms too. Im always Puzzled , when to use 'ln or log'. I've been searching for a good explanation about this topic, but so far no luck. Hope u read this comment 🤞 Reply @SohamSawant-md9gj 6 months ago Thank you sir Reply @ManmohanLeena 6 months ago You are best teacher Reply @colorx_9244 5 months ago Still a bit unclear on getting lucky part. I dont get why rotating the axis would need more components Reply @upuldhanushkagajanayake2719 1 month ago What the hell this is what if I understood this 15 years ago when I was in college Reply @umgeburstet8161 5 months ago When implementing stochsatic gradient descent in you need a batch of (n) samples of image (x,y) pixels of color channel (c). My vectorization works with numpy. Lil too scared of CUDA. Reply @SorokinAU 4 months ago you are genius! Reply @kidenscruton1923 5 months ago Couldn’t you also show tensors as vectors using eulers method? Reply @whattosay385 5 months ago beautiful.. just beautiful! Reply @Bob-v6n3s 2 weeks ago Im an econometrician and I have a question. Can I treat the axes like factors I boiled down from a table of economic data and describe one country or one variable (like inflation) as the stretchable arrow bit (what used to be a vector)? For factors, the metric space (the increments or numbers on each axis) changes as factors SPSS spits out change. Im looking for a way to use tensors. Reply @pythagoras281 5 months ago 0:56 that's the easy part, I got this! Reply @alexanderpacheco6788 2 months ago Genius! Reply @Георги_Лалов 5 months ago Wait what 😅, didn't get it but love the excitement Reply @ragequitredux 6 months ago Ok there was one element of this that still didn't click for me. Because even with just two numbers sigma_xx and sigma_yy you can still have anisotropic behavior e.g. a current moving in a different direction than the field. For instance in your graphene example, you could apply E = <5,5> but if sigma=<<1, 0>, <0.1, 0>> then the resulting J = <5, 0.5>. I still use a 2x2 matrix to describe sigma for the dimensions to work out, but it still wasn't obvious to me why more than 2 numbers are needed. But in your example of J_x = sigma_xx*E_x + sigma_xy*E_y J_y = sigma_yx*E_x + sigma_YY*E_y THAT seems to go beyond just plain anisotropy (different conductivities in different directions) and actually seems to be saying that J_x can depend somewhat on E_y, which is totally trippy because how can a current in one direction be influenced by an E field in a totally orthogonal direction? But I guess it must be the case. Maybe an analogy is pushing a box up a ramp by only pushing horizontally. But that only works because of the Normal force. So I'm guessing there must be something about the crystal's local EM environment that gives the conductivity its own orientation e.g. the orientation of the cubic lattice perhaps. Reply @julianwilliams6735 3 months ago Scattering parameters are a rank n tensor for an n port device Reply @aniket27009 6 months ago It would be much simpler to understand using a 3D stress element. Reply @projectsoup 5 months ago Fascinated by this and started thinking where this might apply in a complex system - (not sure if all of these are correct, so feel free to give feedback): A submarine is diving while under thrust... There is ∆pressure compressing the hull from all directions However, In a dive the nose of the submarine would be lower (not dramatically, though) than the tail of the vessel There is the elasticity of the structure resisting these compressive forces in a gradient along the hull There is propulsion from the propeller that is rotating causing a torque along the axis There is (in a turning maneuver) a torque along the body of the submarine And now the submarine launches an ICBM (removed from the vessel by a high pressure, localized blast of air (i.e., there is no rocket thrust acting inside the submarine to accelerate the missile) and that sudden blast of air, followed by a flooding of water back into the missile housing would cause a localized variation Are tensors applicable here and if so, how many? Reply @CraigHolm 3 months ago Nicely done! If only you can cheer up a little bit. Reply @davidhickerson5 4 months ago What was the name of the Feymann lecture in physics? Reply @jpmorgan5307 5 months ago One mistake you committed E is along x axis in your example, y component is zero then This would work if the axes are not aligned to both E and J Reply @nic3880 6 months ago Nice video This is what torch python had in mind A machine that accepts input and outputs, process with matrixes (tensors) with gpu parallel processing 1) Garbage data in garbage data out 2) modalities increase = increase tensor dimensions (increase n tensors, similar) Reply @SartajX2 1 month ago When /t/ takes a vacation and /θ/ fills in Reply @brianveit7672 3 months ago If the conductivity is zero in the y axis, how can E have ANY component in anything other than the X direction? Reply @user-ug2vw9vb2v 5 months ago i don't undersrtand a thing in this video but i love your passion 😂 Reply @sinistra92 3 months ago considering that each number can be a different special case, then you need the whole universe of numbers to fully define the impedance: at least 3 dimensions, time, density, temperature, gravity/magnetic/etc fields, position of Jupiter, moon phase, age of my daughter, size of the building which manufactured a multimeter..... Reply @Alfirio 4 months ago V = at also does not have to have the two sides be the same direction. Reply @haroutkaterjian9200 5 months ago Great natural world explanation for tensors in AI, where it’s the centerpiece to the whole AI revolution. There tensors get really crazy with 1000 or even 10,000 dimensions. And the “tensor machine” used to achieve such massive computations is the math behind TensorFlow. Reply @BlissOn47 2 months ago I didn't know area was a vector lol Reply @IntegralKing 5 months ago yo you summarized about 2 years of upper div physics in 20 minutes. Can you do Spin next? wtf is spin? Reply @transparent0eye0 5 months ago (edited) This video is fantastic Reply @dummypg6129 5 months ago While debugging my CMake build, i'm procastinating watching what Tensor is. lol Reply @vikrantbhadouriya 5 months ago Hi Mahesh sir! As I approach the end of the video, I was thinking whether tensors could be thought of as matrices on steroids? Essentially because matrices are linear transformations, and as you said tensors of an arbitrary rank n will map two tensors of ranks lower than n with each other. It kinda does make sense to me! Reply @RydarkVoyager 5 months ago Where were you when I was taking General Relativity 50 years ago? Yeah, yeah, a dream in your father's mind... or grandfather's, I know. This was fun, and now I can reread Robert M. Wald's GR textbook again without the PTSD. Reply @saravananb2036 6 months ago Why thumbnail changed