Introduction to Tensors

My tensor series is finally here! In this video, I introduce the concept of tensors. I begin by talking about scalars, then vectors, then rank-2 tensors (whose explanation takes up the bulk of the video since these are probably the most difficult to understand out of the three).
I then move on to define tensors (without specifying their transformation properties), after which I conclude the video with a short discussion on rank-3 tensors, which may be represented by 3-D matrices/arrays.
Questions/requests? Let me know in the comments!
Pre-requisites: You basically need to know what vectors, scalars, and matrices are. Nothing much more to it. A 1st-year Physics + Linear Algebra course should be enough.
Lecture Notes: drive.google.com/open?id=1O5G...
Patreon: www.patreon.com/user?u=4354534
Twitter: / facultyofkhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
- Jose Lockhart
- Yuan Gao
- James Mark Wilson
- Marcin Maciejewski
- Sabre
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
- Bernardo Marques
#Tensors #TensorMath #TensorIntro

[@FacultyofKhan]

If you all liked this video, then make sure to check out the remainder of my playlist on Tensors, because there's more where that came from! kzbin.info/aero/PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_

[@kunalvshah]

Hi, which sw/hw you use for digital handwriting? - awesome video by the way. My tensor concepts are clear now. I have not learned this in my collage.

[@RAJDEEPswarnakar6071]

Bhai mobiel nabar

[@johnkibathi7202]

What software do you use to make these videos, am a huge fan of your eloquent presentations

[@KeyMan137]

I have a bachelor's degree in Physics but we didn't talk about Tensors much. This was an excellent introduction!

[@HighestRank]

Spencer Key phisyxs would be (un)concerned with mostly Brownian motion and other nullificable components. Mechanical(civil) and engineering disciplines plus their common prerequisite transcendent mathematics would need to look more closely at ‘stress mechanics’.

[@jameswood8999]

I have a BS degree in physics too, went to graduate school to learn tensors, more clear here.

[@sidddddddddddddd]

That is strange. We studied tenors in the 2nd year at our university, GR in the third and introduction to quantum gravity in the 4th. It has been a crazy ride.

[@emvee5719]

BSME and we didn't cover tensors either. It's important.

[@lachyt5247]

I don't understand how that's even possible did you not take E&M? Tensors were a huge aspect of Jackson.

[@CazoDK]

This is the best video about tensors on youtube. The only video that covers the actual definition of a tensor: a tensor in _m_-dimensional space at rank _n_ is a mathematical object with components _m^n_., which obeys some rules. Thank you.

[@FacultyofKhan]

Thanks for the kind words! Glad you like it!

[@danmccarron0]

Yes this is a good video - feet-on-the-ground approach which is nice. But, um, no that isn't really the "actual definition" of a tensor. It is how a physicist or engineer would interpret the majority of the ones they use in their applications and rightfully so (except maybe the tensor densities). The subsequent videos deal with those rigorous definitions. Nonetheless this SHOULD be the starting point for introducing them, because antennas and skyscrapers are designed by real people using real equations, not created out of knowledge of differential manifolds or multi-linear spaces and typically they are brought up with those fancy-schmancy ideas in tow. This is good stuff here.

[@JannikPitt]

This is not the definition of a tensor. It's the definition of an m by n grid of numbers.

[@hybmnzz2658]

@@JannikPitt emphasis on "obeys some rules"

[@user-ry1td5uq1n]

@@hybmnzz2658 Everything in math "obeys some rules", but just saying that doesn't tell anything about the particular object. That's why this kind of definition is bad: it can mean anything!

[@Abhisruta]

Your digitised handwriting is beautiful...this may be a Handwriting Tensor Analysis

[@skudzer1985]

I have no idea what's going on, I just found this video in my recommended section, but I love the black background with the colored writing; it's very pleasing to the eyes.

[@icxstudios3169]

same

[@cristig243]

I've got sad when he broke the vector :(

[@enricoiraldo9057]

incredibly useful. In my ignorance so far I always struggled to really find a connection between simple dimensions such as temperature and vectors, always considering them “different topics on the maths book”, but it is now clear how they are linked together

[@isma2605]

This is the most geometrically comprehensive explanation about TENSOR that I have seen on KZbin or books. Finally I realized why the vector's components on same direction can't be added. Thanks

[@sihmidou9843]

A big thank-you ! your videos on tensors are by far the clearest and most intuitive explanations i have found on tensors !

[@feynstein1004]

Amazing introduction. I want more of these.

[@igorxavier1544]

A phenomenal video, thank you very much for the explanation, i could finally understand what tensors really mean!

[@maurocruz1824]

You just broke me free from YEARS and years of misconceptions about what a tensor and its rank really are . Thank you.

[@BMerker]

Amirably clear and concise! Much appreciated!

[@cultclassic999]

Excellent intro to tensors! Thank you so much!

[@mannathugopikrishnan9299]

Perfectly explained. Feeling enlightened.

[@evandrogaio7003]

Amazing. An easy way to explain this amazing definition. Almost all students leave college without a good understand of this

[@HighestRank]

Evandro Gaio everything’s easy to the chimp which didn’t have to produce it.

[@umedina98]

Finally a video which explains tensors in an intuitive way! Excellent examples used!

[@ahmedamr5265]

Finally! A clear and intuitive explanation of tensors. Great job man!

[@MeepMu]

Thank you! You seem to be the only person on the internet who explains what a tensor is from the ground up, and actually gives a concrete example that can be followed and understood by someone who is new to the concept.

[@illogicmath]

Thank you for this video. You are an excellent professor and communicator

[@joluju2375]

Been wondering what it was for tens of years. At last, an explanation with no bs. Thank you so much.

[@HighestRank]

Joluju no bs? It’s Sso fullll of BS that I almost don’t know where to begin. You’re brainwashed by tens of years of being sequestered, and simply suffer from a case of hostage’s-empathy. Torture you much?

[@kshitishp3662]

U are the only one in my life till now I've ever seen who can explain tensors with such clarity ...u are god of teaching ...well done ...and thanks a lot

[@JulieanGalak]

Perfect timing! I just hit the point in my self-study of electrodynamics where I needed to understand tensors. Please release this series quickly! :)

[@HighestRank]

Juliean Galak granted. Oh curse my circuits a whole year late.

[@the_sophile]

Im studying this for General relativity

[@GiI11]

I'm starting an MS in physics in ablut two weeks. Your videos are perfect prep to get back into the game

[@Gismho]

Thank you. This is an EXCELLENT video. All your explanations are SUPERB. I must watch all your other videos on this subject.

[@totakuraanil2921]

Many thanks for a good video, I can see the hardwork you put into editing the video.

[@KevinKuo]

It's a good day when Khan releases a video

[@HighestRank]

The jester was the only other figure allowed to sit in the king’s chair.

[@chronoyeung]

This is the best introduction of tensor i have found in YT!

[@soumya0307]

Now this is something that gave me satisfaction for making me gain the intuition about tensors (Excluding the math part)

[@absolutelynothingtoseehere]

The best intro I've seen so far. Really like the physical examples involving stress, etc. I think that section could be improved by slowing down a bit and going into explicit detail about how the physical forces are mapped to various components.

[@NoNTr1v1aL]

Best video on tensors ever!

[@alikral3149]

Great video! Thank you a million. Your pronunciation is very clear and nice along with the impeccable explanation

[@andcool2]

Probably the best tensor video I 've come across to date. Very elegant and crystal clear explanation of the idea of tensor, especially by bringing up real-life examples of breaking down a rectangular steel beam.

[@HighestRank]

amith anand these days a design would use what are called girders, but for complexity’s sake, a rectangular prism.

[@jeffgalef121]

That was fantastic. Thank you!

[@YourCRTube]

5:25 is why this explanation is the best - it tell you how they are used in practice!

[@ricky12105]

Excellent video. Thank you!

[@trixonx]

With this explanation even a chimpanzee can understand the concept. Very effective. One of the Best 11 mins of my life spent on KZbin!

[@icxstudios3169]

i cant understand

[@eyeballs97]

You just explained what my teacher failed to explain in 3 90 min lectures in 11 minuites. Thank you so f****** much! :)

[@ranitroy6495]

Outstanding....fabulous lecture ...

[@meanymcbeik8082]

Perfect. Thank you.

[@AniketSharmacodes]

I had two questions about tensors after a lecture at my class today, 1. Why are there 9 components and not just add resultant force to 3 component? 2. How is Tensor different from a Matrix? This video answered both of these questions in a very clear and oriented manner. Thanks for understanding what students can be confused about and addressing it right in the first place.

[@HighestRank]

Aniket Sharma you’re not thinking about the same kind of tensors, sad to say.

[@HighestRank]

Aniket Sharma tensor different from a matrix. Well, a tensor isn’t a matrix but it should have one, while a matrix isn’t much like a tensor unless it’s in one. Actually that’s the best explanation I can give after an attempt at listening to billshit’s video.

[@adam-markgheczi4577]

@@declanwk1 I still don't "feel" the difference between them. I don't study physics or engineering, I'm just watching this video for fun. Can you explain why the forces act differently? I can't create a mental model of the scenario.

[@declanwk1]

@@adam-markgheczi4577 sorry I don't understand it myself. If the beam was isolated (in space say) with no external forces then I would expect there to be no internal stress forces. If there was a single force acting down, I don't see why there would be shear forces since there are no components of the downward force in these directions. However beams do thin out when they get stretched, which could be indication of shear forces or just conservation of mass.

[@adam-markgheczi4577]

@@declanwk1 Well thanks for replying anyway

[@IITian_shubham_shekhar_rajput]

Liked 👍 even before I started watching it...this is the level of trust I have with this channel 💕💕

[@HighestRank]

Shubham Shekhar giveitaway giveitaway giveitaway now.

[@josephlam6560]

I am interested in trying to under the general relativity. In order to understand it, it sounds like one of the prerequisites is to understand tensor. For a regular guy with non-physics major, all I know is vector vs scalar. Thank you for this excellent explanation of tensor and I can understand what you are talking about.

[@NancyMancarious]

الفيديو ده شامل تقريباً جميع نواحي الموضوع، شكراً!

[@jokingseverus3221]

The best ever explanation I have ever got about tensor.. thank you so much sir... In particular the explanation of stress tensor was the best part... how easily you told that much tough concept sir...😊

[@PrinceKumar-fe1wr]

Now, my tensor concept is clear. I was wondering about tensor's definition and tried to understand with many sources but failed. Thank you for the video.

[@alphainfinitum3445]

You know very well that you are lying to yourself. This video is as terrible as all those videos and PDF that claim to introduce tensors, but rather take you into some specific application (in this case the stress tensor). At the end of the video you still don't understand tensors in general. Take it from me, if you want to safe your self years of going in circles on tensors, do the following; 1. have a modest understanding of linear algebra. 2. Focus on basis vectors and know how to play with them well. 3. Study forward and backward transformation from one basis to another well. 4. Study covectors well. 5. Study the tensor product well. 6. Then at this stage you will not only know what a tensor is, but you will have a working knowledge of tensors. So you will be able to pick up a book on tensor calculus and follow through well. Good luck and thank me later.

[@ChocolateMilkCultLeader]

One of the best channels for math out there.

[@tareqal-ghamdi1349]

The greatest Tensor’s video ever

[@Martin-iw1ll]

Great video for giving an intuitive understanding of tensors

[@curlyconstant]

Thank you so much this helped a lot🙏🙏

[@TheTranq]

Very helpful and no bs. Thank you

[@mehedihassan8649]

This is gold! Thank you so much

[@abdulmalekwalayeh4790]

What a great explanation!!

[@richardneifeld7797]

Nice clear and simple introduction to the topic.

[@jameswood8999]

Looking forward to the next video. What I'm looking for, is looking for Einstein's application of curvilinear coordinates and using tensor calculus to solve general relativity

[@fitness60plus52]

wow! the best (because VISUAL) explanation of tensors, so different from the usual, axiomatic definition.

[@timothyvaher2421]

Completely realized this lesson. A concise understanding is communicated. Education is happening here: Khan Academy is a towering success!

[@cybertronian9909]

Damn, nice visuals and explanations as always

[@lucys3482]

Excellent video. I love the beam example, as it puts the concept into a real world problem. You clearly have a charisma in passing on your knowledge. Not many have the 'touch of Feynman'. :) Thank you for doing this!

[@RyanLBuchanan]

Brilliant! Thank you soooo much! Now I understand!

[@jurascipakre9200]

Best explanation on youtube, thank you.

[@ankurc]

very simple and clear thanks

[@lunacui461]

Thank you SO MUCH!!!

[@ibanix2]

jesus christ, this was the video I needed. Simple, concise, perfect illustrations.

[@rachanasoni007]

Your voice and fluency are 😍

[@prashanttripathi2211]

Thank you so much sir. Wonderful explanation

[@hendriaditjandra6418]

Thank you Sir for a very clear explanation.

[@serahstales9451]

Thank you so much sir🙏🙏

[@MathwithMunaza]

Best explanation on this topic.

[@thomasanderson1416]

FINALLY! Thanks.

[@rp1455]

Thanks for just giving it straight. This was a much more helpful explanation than others who used fancy graphics or kids toys.

[@ezu8501]

great job! beautifully done. and your digital handwriting

[@eoinmullally1531]

Great Video! Very neat and easy to understand!

[@NovaWarrior77]

LITERALLY AWESOME.

[@soumahakase7124]

You are a bless man, thank you very much.

[@ParasiteDelta]

You melted my brain, but it's still very interesting. Well done.

[@nargis7646]

Great explanation...Thank you

[@gunaycafarova750]

Thank you for this video , I think it will help me in my speech about Tensors✨

[@mokshraj63]

I really wanted to have this lecture thank you sir pls add more videos of Physics 💙

[@wdobni]

this guy is a TEACHER ..... very good video that reduces tensors to reasonable ideas for simple minds like mine

[@Abhisruta]

Very good video... All concepts are clear

[@amitshoval7653]

Thanx for an this amazing explenation!

[@gerardomoscatelli8584]

Amazing explanation tks

[@rahuldas4967]

Shit this 4 year old content is much better than all the videos I watched on Tensors till now ❤️😍

[@kewal_chhetri]

Very nice introduction to tensors... Impressive.... Explained in a very fundamental way

[@PunmasterSTP]

This is hands-down the best explanation of tensors that I have ever seen or read. I can't tell you how much time I have spent in different places looking at different things and still not understanding the essential concepts. Thank you so so much for making these videos and putting them up, and I'm planning to binge-watch them in my free time!

[@infinitylove2713]

Nice lecture.......keeeep doing .....it will help a lot ..thank you sir

[@GandalfTheBrown117]

Very well made video. I like the script and examples and the figures were drawn very well. Thank you for this.

[@FacultyofKhan]

Thank you very much!

[@RAJDEEPswarnakar6071]

Bhai moja lol dado mara uid 2022826303 Subkrieb kardaia

[@sindbadthesailor1541]

Great video!!

[@ErickFGx]

Thank you!

[@JoseAntonio-ml8yg]

¡Gracias!

[@fmp1976]

Great lecture, thank you

[@Zeezoro]

Best video. Thank you

[@Gabby-du4mc]

You are a blessing!!!!

[@mrozzy4442]

Very helpful - thank you!

[@hankli6968]

the best video on tensors!

[@rfzafar]

The insight for tensors was amzaing, i was struggling to solve a problem which included gradient of exponential function in matrix variable.

[@user-te4jj2nq6q]

Very nice. Thank you 😊

[@karthick...]

Thank you ❤️

[@zubairahmad655]

Thanks a lot sir. U have solve my a lot of my problems..

[@somefuckstolemynick]

Great video! Thanks!