What's a Tensor? 2,790,435 viewsNov 20, 2011

What's a Tensor? 2,790,435 viewsNov 20, 2011 Dan Fleisch 37.1K subscribers Dan Fleisch briefly explains some vector and tensor concepts from A Student's Guide to Vectors and Tensors 4,337 Comments rongmaw lin Add a comment... berat postalcioglu berat postalcioglu 1 year ago Brilliant and simple explanation. It reminds me the quote: "If you can't explain it simply, you don't understand it well enough." 570 Todd Newton Todd Newton 1 year ago No Mr. Fleisch, thank you for YOUR time. Without exaggeration, this is one of the best educational videos I have seen on any subject: evenly paced, concise, clear and direct. 89 Brendan Larson Brendan Larson 1 year ago This man is so wholesome. We must protect him at all costs. 1.2K Prajwaldeep Kamble Prajwaldeep Kamble 1 year ago Can anyone take a minute to appreciate how beautifull he made us visualise vectors without animations like 3b1b You really can't tell which is better both are great teacher. Sir Feynman must be smiling from above. 277 Karthik Naig Karthik Naig 10 months ago Extremely well explained...I wish we had more teachers like him. 14 Richard Richards Richard Richards 1 year ago This guy is proof that if you want to teach, it's not enough for YOU to know your stuff-you have to have the ability to communicate it to those who DON'T know. 120 Primata Falante Primata Falante 3 years ago Such a masterpiece in science communication! Saw it the first time years ago, when I first started to learn Tensor Calculus, but I still learn something every time I watch it again. 690 Philip Philip 9 months ago I love how he delivers a very basics oriented explanation trying to really explain it well and then as motivation in the end drops two sentences about reference frame transformation that no one with only basic insight into the topic will understand even remotely XD 20 iliketrains0pwned iliketrains0pwned 7 months ago Thank you so much! I'm taking Advanced Aerodyamics and Aircraft Structures this semester, and it's my first time hearing about tensors. You really helped me intuitively understand what they are much more clearly than my professors could through mathematical proofs and linear algebra! 4 AI Quotient AI Quotient 1 year ago This is probably the best explanation of a 'Tensor' out there! Great illustration of the 'Feynman Technique'. Thanks, Dan for all the effort! 37 Himanshubhusan Rath Himanshubhusan Rath 9 months ago Sir, you are awesome. I can never think of such concepts to be explained in such a detailed and clean way! Thank you so much for your effort. Simply what a beautiful teaching style. 2 Noah Hysi Noah Hysi 1 year ago Thank you Dan Fleisch! I'm on my way with learning Linear Algebra but I've never come across an intuitive explanation of a tensor until now! 10 Ralph Dratman Ralph Dratman 6 years ago This video is a good example of the educational riches accumulating on youtube. In fact I hate to use the word educational, because it might evoke stiff, uncommunicative academia. But the learning culture on youtube is just the opposite of that. Here we find people passionate to pass their understanding along, filling in a thousand little corners of knowledge. I think we are in the early beginnings of a historical period in which the internet rewrites most of the rules and experiences of human society. I find it thrilling to be living in such an amazing moment. 6.6K Rayman Goel Rayman Goel 8 months ago I am very very grateful to you sir !! Never ever expected such a beautiful explanation to rather seemingly concrete mathematical idea . You are an inspiration to the generation of teachers!! ☺️🙏🏻 1 Amy Li Miller Amy Li Miller 1 year ago Just to let you know, I read your book to the end. I had a good understanding of vectors, including the dual vector concept and tensors. I am now studying general relativity and your book has jump started me.Thanks Prof. Fleish for such a wonderful book. 1 Harrison Hilbert Harrison Hilbert 1 year ago Two things we know: What a tensor is Who not to challenge to a nerf war 1.2K TS-TLF TS-TLF 11 months ago I enjoyed learning from this video. it is simply so immersive. masterpiece. Thank you Prof. Dan. 3 Abhijith Arakali Abhijith Arakali 1 year ago (edited) Wonderful content! It's a humbling experience to watch a highly knowledgeable person present this concept in an effective way. Not only that, but it is obvious that he is very passionate about the subject. People who have great passion towards anything as deep as differential geometry are truly blessed. Thank you for taking time and putting in effort to explain tensors! 2 Gil Zam Gil Zam 3 years ago I love how he says at the end thank you very much for your time, when in reality he went out of his way to try and express tensor in laymen terms for us. 2.1K Captain Vita Captain Vita 8 months ago I wished i had such a great tutor when i was studying EE and CS. Thank you so much for this great explanation Dan! 1 Juan Francisco Jesús Hernández López Juan Francisco Jesús Hernández López 5 years ago 👌👏👏👏👏👏👏👏👏👏👏👏👏👏 this is a great methodology, it is a mix of old school and new media, but what really makes this awesome is the professor's attitude and charisma. Keep on doing an excellent job. 👍 419 Kab Kab 1 year ago Well done sir, thank you. Starting with this approach (vs just getting into the proofs straight away - which is mostly how higher level math has been taught to me) is so excellent to build a basis for visualization of future calculations because you have "linked" tensors to the real world. 💚 from Canada 🤓 1 Roland Schweiger Roland Schweiger 8 months ago thank you for the straight-forward video - it really helped me to understand, though i am actually doing some programming myself. very comprehensively explained, well done! 1 Debashish Chakraborty Debashish Chakraborty 1 year ago Thank you sir. Being a teacher myself, I am overwhelmed and deeply moved by your knowledge and style of presentation. I recommend this video not only for novice students but also for experienced teachers. 1 Josh Bloom Josh Bloom 1 year ago That was awesome. I've been a high school physics & astronomy teacher for 20 years and have a degree in Physics and Astronautical Engineering but never really had to work with tensors (beyond vectors). I've always known about them (but never worked with them) in the context of General Relativity. This is the first time I've seen it explained in a way that makes (mostly) total sense. If I ever teach an advanced Astrophysics course I will have to include this video. Thank you for taking the time to explain it so clearly! Manoj Pradhan Manoj Pradhan 1 year ago This was the most intuitive, concise and clear explanation of Tensors I could find. Thank you very much for putting this online for us. 1 Oliver Becerra González Oliver Becerra González 5 years ago Professor Fleisch. First of all I want to congratulate you for such a simple yet wonderful to explain what a tensor is. I wish I had a professor like you during my bachelor, because people like you, that devote to make complex concepts easy to understand to people are true Masters. I am looking forward in the future if you could upload more videos like this. 24 S Ram Kumar S Ram Kumar 10 months ago This video explains things so crystal clear. Thanks for uploading! 1 Composer Composer 1 year ago Very well done! My compliments! I am a nuclear physicist, and I love the skill with which you described these complex subjects in a way that is understandable to someone hearing them for the first time. 1 Stephen Hobbs Stephen Hobbs 1 year ago Outstanding video. Really simple to understand. Thanks, Dan!! 1 Al-khatab Ali Al-khatab Ali 1 year ago this was so informative, I learned more things in those 12 minutes than my entire time in linear algebra and calculus courses in college, this is such a great teaching method it made this relatively complex and theoretical concept into something real that you can relate to I don't think I will forget this concept anytime soon. Saad A Saad A 1 year ago Beautifully explained ❤️ thank you professor!! 1 Benjamin Cordes Benjamin Cordes 5 years ago Dear Dan This video really helped me understand tensors for my course i solid state physics. I liked that you used physical explanations because they are very intuitive and easy to remember. I would love to see you make a video about eigenvalues/eigenvectors in a similar style. I know this has been mentioned before in the comments and it's another very important concept in physics and mathematics that a lot of students have problems with. PS. Please don't take rude comments seriously and I hope they don't discourage you from making more videos that would be such a shame. With half a million views you are going to get comments from some sad immature people. I would bet that 99.9 % of people watching this video found it helpful and are very grateful. (as reflected in the many views and likes) 12 Juan Nunez Juan Nunez 3 months ago Very well done; I'm still left with questions, however, that's on me as I can tell you've simplified this topic as much as possible. Thank you, Sr. Devansh dhar Dwivedi Devansh dhar Dwivedi 6 months ago Sir, i can't be thankful enough. This was such a mind blowing explanation and there were tears in my eyes when it clicked that what an amazing concept it was.i really owe you a lot. You are the best teacher. I am literally never gonna forget you.... ❤ Gholam Baghery Gholam Baghery 1 year ago So great. Thank you so much master for this professional video. it is so amazing that you can show a complicated issue with some simples devices. it's great Kouroush Sadegh Zadeh Kouroush Sadegh Zadeh 1 year ago Such a great teacher! With his explanation, even a high school student can understand what a tensor is! Bravo! Ashfvt Ashfvt 1 year ago Thankyou very much sir. You explained it very simply. I have tried to read textbooks to understand tensors but none of them ever made much sense. It is very thankful of you to share your knowledge with us. 1 Alley00Cat Alley00Cat 5 years ago The power of representing data as tensors is that you can do matrix algebra on them. If you program, you'll appreciate that this decreases computation time by orders of magnitude when compared with loops. 38 ELOISIO MARQUES DE MORAES ELOISIO MARQUES DE MORAES 1 year ago Uma brilhante exposição sobre tensores , um dia ainda irei estudar este conteúdo profundamente. Nico Robin Nico Robin 2 years ago You can feel him putting a good heart into his explanation, ❤ 97 Hritik Gupta Hritik Gupta 5 months ago This was so well explained. Thank you so much! Preeti Kharb Preeti Kharb 9 months ago This is the best thing I have seen on YouTube. The way he has explained Tensors, can not imagine a better way of doing that than this. Thank you so much!! 1 P S Yee P S Yee 1 year ago Thank you, Mr Fleisch. A very well-presented video. A wee bit too much on the simple vector stuff, and I was very happy to understand the higher ranked tensors. It was a bit rushed towards the end, just when it got really interesting. A bit more explanation on how rank 3 tensors could be used in practice, especially shear forces on surfaces would have been greatly helpful. If only my professors explained half as clearly as Mr Fleisch... I remember how I struggled with the Ricci tensor when digesting general relativity. Guylaine Doucet Guylaine Doucet 7 months ago Thank you so much M. Fleisch. It is the first time I learn something about tensors. I never heard the name of tensors before...but I think I learn more in 12 minutes than with a full book on tensors...Guylaine from Quebec Canada 1 Florian Wirtz Florian Wirtz 1 year ago Amazing explanation. In two hours of lectures I couldn't understand what I just understood in 12 min! Thank you! Mr Gaudy Mr Gaudy 5 years ago Educators like this are worth their weight in gold, particularly when dealing with the often abstract and seemingly intangible concepts of mathematics. Great demonstration. 5 heidioid heidioid 5 months ago I wish my professors explained tensors like this… I need to re-watch the last half to fully get his words, but the cubes and unit vectors on the table really help me visualize the acting forces. Wow. Definitely gonna check out his book. Thanks for sharing this!! 😃 Abhinay Raikar Abhinay Raikar 5 months ago I'm a Mechanical Engineer yet never learnt about Tensors, thank you for explaining so well, sir Brian Perry Brian Perry 1 year ago A wonderfully clear, transparent introduction. Has Dan Fleisch done a video on covariance, contravariance and rank? bimal khatri bimal khatri 1 year ago Watched the video again after 4 years and still I get amazed seeing his dedication to teach us in the video. Magnificient!! Lakshmideva l Lakshmideva l Lakshmideva l Lakshmideva l 1 year ago Thank you very much for your incredible teaching sir ,it help me a lot to understand tensors ,sir Tracchofyre Tracchofyre 3 years ago mechanistic explanation of a very abstract mathematical object. Beautiful and very effective. 169 Methadras Methadras 1 year ago This is the best expression of Tensor I've seen to date. it was so simple and easy to follow that I now have a full understanding of them. I'm now visualizing all kinds of things because of this explanation that I didn't connect before. Fantastic work, Mr. Fleisch. Thank you. Deoraj Singh Deoraj Singh 1 year ago This is something that completely changed my understanding of vectors and I thoroughly agree that Tensors are "the fact of universe". Thank you so much for this video. Sergio Lucas Sergio Lucas 4 months ago What an amazing video, so simple and functional :) Saroj Singh Saroj Singh 1 year ago Just amazing ...best teachers make you love learning. Huge respect Matteo Archimi Matteo Archimi 1 year ago Thank you very much for your expla