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Dan Fleisch briefly explains some vector and tensor concepts from A Student's Guide to Vectors and Tensors

Text Comments (2518)
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D L (17 hours ago)

Thank you!!!

12B (1 day ago)

column vectors with baby blocks. that's good abstracting!

Tridosha c Borthakur (1 day ago)

Love your teachings sir

Soap A (3 days ago)

Can we get some tensors to not upload a video in 360p?

Ahmed Syed (3 days ago)

thanks

jmw150 (7 days ago)

No... the opposite. I want stupid physicists to just explain what they actually mean by tensors. And you still did not talk about the algebra of tensors. Any idiot can say it is just a vector of vectors ... of vectors.

Aldof Hitle (8 days ago)

I want to be good at math, please help me

isambo400 (9 days ago)

If you think this is interesting, I can teach you how to make a bomb out of a toilet paper tube and a stick of dynamite

stratton.t (10 days ago)

Vectors can represent area (with the magnitude being the size of area and the direction being orthogonal to the surface of the area). If you have ever been to college you can now skip to 7:48.

Ridhun Murali (11 days ago)

Tensor in 3 dimensional space is ok... tell something about tensor in 'n' dimensional space.

Peter Riis (12 days ago)

So, what is a Tensor?

babar javed (17 days ago)

that's the awesome way to teach. but i am till confused about the triads. kindly tell me some applications of it. Thank you.

Shreyas Joshi (20 days ago)

Dr Dan Fleisch, This video is amazing. However, I am still struggling to understand when do you need tensor 2 like 9 components. I still didn't get it. Like, you said some forces. I couldn't understand that part. I will appreciate if you could elaborate on it. Like, I am looking for practical things where you need tensor 2 or tensor 3 with some elaboration on it. Please help.

Tim Brittain (20 days ago)

Thank you for this video! You did an excellent job describing what a tensor is without getting lost in the mathematical transcription. I now have a better inutautive feel for what tensor safe and how powerful they are. Basically, you can describe multiple aspects of a system using tensors. So, if I want to describe how light, gravity, and the earth’s magnetic field interact at the earth’s surface I can do so with four basis vectors. One for each system.

Paul Catling (22 days ago)

Took me five minutes to realise he was saying "component" and not "complement". Very unusual pronunciation of that word.

Paul Dirac (23 days ago)

Ophello, I apologize. My intention was not to criticize you but to inform. You are correct. I am a horrible speller. Linear Algebra, vector analysis, and matrices will give a good foundation for tensors. Basic differential geometry would be a plus.

gaussagain (24 days ago)

If only he had pronounced 'components' as com-PON-ents.
As it was, COM-pon-ents DIS-tracted me!

kandysman86 (24 days ago)

I've found that learning CS and programming languages has led me to understand higher level math better than I ever could have. I can draw so many parallels, it has taught me how to learn the rules of mathematics. This is a really cool development.

cloudbear (24 days ago)

So the x component of the vector is the x component of the Manhattan distance from the start of the vector to the end, and likewise for the y component, and so forth?

Shinobi_Tactics (24 days ago)

I don't know why I'm watching this but here I am.

José Eduardo Teixeira (24 days ago)

That's Brilliant!

Gunnar Kossatz (25 days ago)

Burkhard Heim based his TOE on Tensors

vocalnerd (25 days ago)

This is an incredible video.

William DiBlasi (25 days ago)

My compost pile is full of components

Zwölfenbein (25 days ago)

I find this more helpful: https://www.youtube.com/watch?v=CliW7kSxxWU

Paul Dirac (25 days ago)

You have a wonderful mind. Pure genius. Back to geometry.

Page Fault (26 days ago)

Now let's add another dimension, make that an infinite number dimensions.

Adin000 (26 days ago)

Great video!

LimeTr33 (26 days ago)

Aᵧᵧ lmao

Icon Icon (26 days ago)

I'm a absolute beginner on this but kind of thrilling

hytlerson (26 days ago)

still too complicated for me

Puvendran Pillay (26 days ago)

A_xxx -> xxx tens(ion)or

Kenny Rowe (27 days ago)

Gucci gang tensor?

Idjles Erle (27 days ago)

I got 100% on my 3rd year general relativity exam, and this is the first time I've seen tensors explained. I never saw them before - I just knew they are what took Einstein 10 years to get from Special to General Relativity.

Santa Paula De Roma (27 days ago)

Clear and concise, thanks much Mr.Fleisch.

dgetzin (28 days ago)

<lighter held aloft> Duuude! Pythagorean theorem, play the pythagorean theorem!

ansishihi (29 days ago)

7:32 is that NERF gun ammunition? >_>

ofeyofey (30 days ago)

Would be great if you could similarly talk through covariant and contravariant components, thanks for this video though

ofeyofey (30 days ago)

Prof Fleisch, Your books are brilliant, I only discovered them recently, thanks

murug anand (30 days ago)

thnks very much for your time

Arindam Das (30 days ago)

The Azzz should have 3 Sticks...instead of Only 2.

Prashanth Kumar (1 month ago)

Good sir..

ophello (1 month ago)

I still don’t understand tensors.

Sho Am (22 days ago)

+Anderson 63 Scooper Surely you're joking? It's a joke about *Tense* right, not *Tensor* ?

Logan Andrews (23 days ago)

I still don’t understand why the earth is flat

ophello (24 days ago)

Paul Dirac learn to spell before you criticize the intelligence of others.

Aiden Murphy (25 days ago)

+Paul Dirac You insult most of humanity while not being able to spell and spouting nonsense too. You sound like a tool

Paul Dirac (25 days ago)

Most minds can't understand simple mathematics. The ediot that wants more explanations, is a ducking editor. Mathematics is not liberal. You get it or you don't. Teacher used simple Cartesian geometry to explain tensors.

Big Fuss (1 month ago)

First time ever I see a light shadow to represent a projection of a vector. A very unimaginable way to make an easily imaginable thing more unimaginable.
And in simple words, tensors are the mathematical representation of transformation coefficients between two (or more) geometrical coordinate references. Suppose you have vector in the Cartesian coordinates (xyz world each is perpendicular on each), and you want to transform that vector into some curvilinear coordinates (say uvw world that differs from the xyz world); then what will you use to write the components of that vector? Right. You will use a pen and a paper. Bravo!

Pat Vdp (1 month ago)

Ok so ... what is a tensor ?

Gaurav Ragtah (1 month ago)

Excellent video!

MrUsidd (1 month ago)

YOU ARE ONE GREAT TEACHER!

Yohei Tanaka (1 month ago)

I couldn't get main idea what the tensor is, just now I got it !! thank you so much!!!!!!

Mark Warner (1 month ago)

so a tensor is a matrix of a vectors components ? ...

Osman Khalil (1 month ago)

isn't unit vector is unitless ?

Boris Mezhibovskiy (1 month ago)

As a computer programmer, I understand vectors well enough to do lots of fun things with them. I still have no idea what I would use a tensor for, that I couldn't use a collection of vectors.

Victor Selve (5 days ago)

Chemistry

Ganesh Kumar (11 days ago)

+NANDAKISHOR M lul

NANDAKISHOR M (11 days ago)

Ever heard of tensorflow

Mohd Asif Khan (1 month ago)

So practical, thanks a lot

doublestarsystem (1 month ago)

Great job professor...i am no longer afraid from the word tensor as i was befor...although i have to dig deep into this subject to grasp its meaning...i think tensors were used by Einstein to formulate his math equations for relativity...with the help of one mathematician...because Einstein was more focused on physics theories than the math that support it...Thank you man

DemonLordChaos (1 month ago)

a tensor is a vector where every component is a vector or matrix?

Golib K. (1 month ago)

Are shadows and reflection can be interchangeable in this scenario?

The TruManZoo (1 month ago)

ive been told the well known formula e=mc2 results in a tensor, is this correct?

Strong (1 month ago)

When you're gone so high in math, that you forget to use rectangular pieces on table instead of circular ones.

Elias Ajenifuja Ibrahim (1 month ago)

THANK YOU!

0B ZEN (1 month ago)

Plenty of Nerf gun ammo laying around the house... Don't mess with this badass.

N DCSydney (1 month ago)

Awesome, awesome and awesome!

CastelDawn (1 month ago)

well...now i know

SNoCappidona (1 month ago)

i liked how you used the light and shadows to show the magnitudes of the x and y components of the vector as the angle was changing.

smoothoprk (1 month ago)

What's the application for rank 3 tensor, when rank 2 tensor is able to describe 3d objects?

Chris De Christophe (1 month ago)

If you need this level of explanation you’re in trouble! Clear, but laboured

Chris De Christophe (1 month ago)

Zee?

Ben Kennedy (1 month ago)

Wow, excellent video.

Dan Ryan (1 month ago)

Stunningly excellent. Nicely done, Dan. Your students are lucky!

Olumide Oni (1 month ago)

OMG

Texan (1 month ago)

Most clearly articulated explanation I have ever got on Tensors. Dan, you are doing such a great service by posting these videos in you tube. Greatly appreciate your effort and looking forward more great videos. Thanks.

xy9izzy (1 month ago)

This is great, I love the visual and physical tangibility of the examples. More advanced stuff starts around 8:45

Marco Gallone (1 month ago)

Technically, unit vectors are unit-less. The scalar quantity you multiply a unit vector by is the one with units. If you say that the unit vectors have units of some dimension one might make the mistake of dually accounting for units or oddly performing unit conversion to make them align, which is simply not the case. The definition of a unit vector is a position vector (described as some vector with known length and direction from the origin) divided by the magnitude (or the length) of that position vector so the net result is unit cancellation with the magnitude of the new vector to be simply 1, along the same direction of the original position vector.

privet vastutnestoyalo (1 month ago)

Fifteen years later, I finally understand what the hell I was working with all this time after graduating.

Md Khaled Hyder (1 month ago)

There is no better explanation than this. Thanks a lot

Charles Stacy Harris III (1 month ago)

This was fantastic! I'm going to use this method if I get the opportunity to tutor again.

ARIVILIAR (1 month ago)

Well explained, amazing content; crystal clear :)

Joe Smith (1 month ago)

I learned how to manipulate tensors pretty well. But now I think I understand them. The last bit about reference frames was the "Oh, I get it " moment. Few decades late. That's OK.

Robert Smith (1 month ago)

OK Dan, you are obviously a fan of Andy Rooney. Who keeps 27 darts in their house?...and why are they called: "tensors"? Seems like they should be called twentyseveners. Oh no, I think I broke my Hamiltonian. Nice job Dan. :-)

Richard Herbert (1 month ago)

0:30 Monty Python pronunciation of "... a pointed stick."

batmanbutbetter (1 month ago)

Nice table

Maria Callous (1 month ago)

I just see children's building blocks...I don't have the necessary genetic material to understand vectors. I cannot build rockets.

jef (1 month ago)

This video has been coming up as recommended for at least 8 years. Today, I will finally watch it.

Kate Moon (2 months ago)

You took a concept that is very difficult to understand by us mere mortals and made it easy. You are a super guy.

Rob Colclough (2 months ago)

So tensors are arrays of basis vectors, but arrays of vectors is nothing new. Why are tensors, or 3x3x3... arrays of vectors useful?

whatshendrix (2 months ago)

Why do people insist on making the most convoluted explanations for the easiest most intuitive shit?

SINC0MENTARI0S (2 months ago)

This is a very humbling, sublime explanation by a generous human being. Perfect video.

Sina Ghafouri (2 months ago)

Beautiful 👌

John Smith (2 months ago)

Which phenomena is 3 tensor type??

abcdyou (2 months ago)

please do some more videos using real life objects. I understand Tensor very well. Thank you Professor

Matt-Klaus Mushi (2 months ago)

Thank you!

basnicy1 (2 months ago)

do people know how beautiful this demonstration is?> It takes reasoning via examples and magnificently paints out images and understanding in a learner who is not an engineer...so beautiful..thank you, truly

basnicy1 (2 months ago)

it gets superbly useful at demonstrating the representation at 10:50 in the video..a delight

Rounak Mohanty (2 months ago)

Best explanation ever

Rich Hlywka (2 months ago)

You University kids don't understand it and it's too hard... not a problem...
Here are some building blocks meant for a 4 year old.

Euquila (2 months ago)

10:33 Dan: "I'll zoom in a little bit here so you can see the..." Me: "OH GAWD MY BRAIN!"

niwa (2 months ago)

Wow. This is one of the best educational videos I have ever seen. Thank you, Professor Fleisch!

K. Chris Caldwell (2 months ago)

Superb!
Thanks.

Kris Warren (2 months ago)

This video is fantastic....thank you Dan

Gilberto Zamarron (2 months 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.

Paul Xie (2 months ago)

It would be better to combine the vivid presentation with a little mathematical expressions so specialists can benefit more from the video. But overall a good one.

Leo Kovačić (2 months ago)

A tensor is simply a multilinear map you fucking coordinate dependent retard

Mallikarjun Aralimarad (2 months ago)

Thank you

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