0:40 I swear to god this is pretty much the explanation my teachers gave me. "Tensors are things that be like they do, but only sometimes. anyway here's your homework, you little shits. enjoy "

General of Relativity: a thing that behave just like the general of relativity

@leonardodias3393

3 жыл бұрын

Well, no. But actually, yes.

Hey, man! You have very clear explanations on a very subtle topic. Keep it going!

Amazing videos as always. Please keep it up with upper-year undergraduate physics and math courses!!!! Love it

This will be a good Saturday evening :)

0:40 I feel targeted, hurt, and generally unsettled, all of which are made up for by the rest of this video.

@FacultyofKhan

6 жыл бұрын

I'm glad that you share my feelings towards that definition.

@gregoriousmaths266

4 жыл бұрын

I would like but ur comment has 46 likes

@mastershooter64

2 жыл бұрын

It makes sense once you learn the maths behind it lol that definition isn't really meant for people who are learning it for the first time, just like this definition of a vector "A vector is an element of a vector space" it makes sense once you know what a vector space is.

This is by FAR the best series I have ever found explaining tensors in a very clear and concise way that isn't only the math but the intuitive explanation behind the maths. Subbed and liked!

Thank you again for giving the clearest explanation on this topic that I have every heard. Finally, when it comes to working with these things, I'm not as...tense!

excellent video. very clear conception of a tensor and a lucid explanation

0:40 Every 60 seconds in Africa, a minute passes

@alwaysdisputin9930

2 жыл бұрын

Clocks tick faster at the top of Mount Kilimanjaro. You can fit 1 million Kilimanjaro seconds into 1 sea level minute

You deserve more subscribers, I really hope that your channel grows and get known, your explanation is really good and you cover university topics that are fairly hard to find and whats more, that are explained that well. Tensors were a total nightmare for me to understand and you really saved me from drowning in that topic. Thanks a lot!

@FacultyofKhan

5 жыл бұрын

Thank you! Share my videos with your friends to help me become more known!

best ever video for tensor ，thank you sir

love to hear u ...it clears my all concepts about tensor

Awesome video sir. Your efforts are really appreciated. I love your channel so much

Thank you! Now I know more about tensors!

this is perhaps the clearest guide to anything on youtube - thanks :) (applicable to part one as well!!)

wow, it just clicked I know what tensors are now, thanks!

The best video explaining clearly about the behind the scenes that happen during a transformation of a tensor. Thanks for this great video . Also could you please refer me to any book where I can learn more about Tensors

@FacultyofKhan

5 жыл бұрын

Schaum's Outline is one good option for beginners. Good luck with studying!

Anthony Zee: A tensor is something that transforms like a tensors...

@HighestRank

4 жыл бұрын

黄瀚 “noshit,Sherlock”

@MsAlfred1996

4 жыл бұрын

That's actually not the true definition of a tensor. Given a vector space V and its dual space V*, then a tensor T is just a multilinear map such that T: (V ⊗ V*) --> ℝ All properties can be deduced from that. It's a much more elegant and rigorous way of defining it. But of course, it's less intuitive and imposible to understand if you're not familiar with linear algebra.

@shinzon0

4 жыл бұрын

@@MsAlfred1996 No it is not... It might be "elegant" with regards to writing or abstract formalism, but surely not for understanding. It is exactly this crap that kept me busy for years. Also if you try to understand General Relativity, it would be much better to use Geometric Algebra, then you even don't need tensor stuff to solve some things. It is a problem of modern science to get more and more abstract instead of relating things to a simple understand, WHICH IS STILL POSSIBLE! If definitinos lead to the same things, and principles, then there is no TRUE definition. There are always several definitions possible.

Great video series! subscribed

You did a marvelous job... Greetings from Nigeria..🤝

These videos are honestly the best resource I've found explaining what tensors are. Thank you!

Very useful video for understanding!!)

This is some of the best handwriting I've seen from a lecturer. Some of mine had very messy handwriting, or didn't fully erase previous boards (just lightly rubbed out), so I spent a lot of the time trying to work out what was written on the board!

@FacultyofKhan

Жыл бұрын

Wow, thank you!

These are one of the finest ed videos I have ever seen. I'm glad that the topic is discussed so finely. Great job!

What is foo? Foo is an object that transforms like a foo. OK...

Coordinate systems are used to describe reality. A change of system changes the description, but not reality!

@_DD_15

4 жыл бұрын

Clap clap clap. Nicely said

@jacobvandijk6525

4 жыл бұрын

@@_DD_15 Hahaha ;-)

Thanks a lot. Hope u channel got at least 1M subscribers :)

You and 3blue1brown are making my move from Electronic Engineering to Mechanical Engineering a pleasant walk in a wood. Thanks man!

thank you, love khan

props my dude, you are ridiculously good at explaining shit

cool tut!!!

0:40 "Ah yes the floor here is made out of floor"

Thanks for you

Along this series resource, KZread and internet really evolves on how people learn. Great Videos on tensor you made. I often think tensor and matrix are actually same thing. But it is not. One question I have, when you notate tensor from the cube surface one by one, you write them down in matrix form from the first row to the third row. Why not write down these surface breakdown components in column ? From the left first column to the right.

Goteeeeeem!

This is an extremely coordinate-centric point of view of tensors. I don't think much can be learned about them until you understand the basic, abstract definition of a tensor product. Otherwise, the change of coordinate rules (which aren't even actually explained here) will seem mysterious and unmotivated, and hard to remember (so many coordinates!). Tensor products, abstractly, are *really easy*. A general element of the tensor product, let's say of vector spaces V1, V2, ..., Vn, is just a linear sum of terms (v1,v2,....,vn), where each vi is in the vector space Vi (in the video, each Vi is R^3, which is of dimension 3). So a general element of the tensor just looks like a.(a1,a2,...,an) + b.(b1,b2,...,bn) + ... + z.(z1,z2,....,zn) where the a,b,...,z are just scalars and, again, the ai, bi, ..., zi are in the vector space Vi for each i. This is subject to some rules: Firstly, you have distributivity: R1: (x+y,v2,v3,...,vn) = (x,v2,v3,...,vn) + (y,v2,v3,...,vn) and similarly if you split in coordinates other than the first one. In other words, you can combine two tensors which disagree in one coordinate by combining the answer in that coordinate. Secondly, you have scalar multiplication: R2: c(v1,v2,...,vn) = (c.v1,v2,...,vn) and similarly if you choose a different coordinate. In other words, you can bring multiplication by a scalar into (any) one of the coordinates. We also implicitly assume that (c1+c2)(v1,...,vn) = c1.(v1,...,vn) + c2.(v1,...,vn), for scalars c1 and c2. Now, if V1 has a basis of vectors b1, b2,..., bd (so V1 has dimension d), then we all know that a general element v1 in V1 can be written c1.b1 + c2.b2 + ....+ cd.bd. It follows that a general component like (v1,v2,...,vn), where each vi is in Vi, in the tensor product can be rewritten c1.(b1,v2,...,vn) + c2.(b2,v2,...,vn) + ... + cd.(bd,v2,...,vn). That is, you can split your v1 as a sum with respect to the basis for V1 and distribute in the tensor. You can now split each of these terms in the V2 component given a basis for V2, each of those can then be split for V3,... and so on. That means that you can always express an element of the tensor product as a linear sum of elements (e1,e2,...,en), where each ei is a basis element of Vi. These are linearly independent, so one sees that the tensor product of V1,V2,...,Vn is of dimension dim(V1)*dim(V2)*...*dim(Vn). This is opposed to the dimension of the standard product, whose dimension is the _sum_ of the dimensions. Anyway, that was longer than expected! But the point is: 1) the rules for the tensor product are really easy if you just give the abstract definition. There are just two rules R1 and R2 you need to know really. 2) you can choose a basis for the tensor product by choosing bases for each vector space you're tensoring, and a basis element for the tensor then corresponds to choosing one basis element for _each_ vector space (in the video, each Vi has the same dimension m, so the tensor has dimension m^n) 3) anything else, such as changes of coordinates, can (and in my opinion *should*) be easily derivable from this basic definition. You can start with the coordinate-wise definition, but I think that this approach encourages people to think of tensors as just high dimensional arrays of numbers, which is _not_ a good intuition.

@evanurena8868

4 жыл бұрын

After reading you're explanation on tensors and comparing it to the video, I now realize that this video relies way too much on the geometric point of view without focusing more on the linear algebra aspects of the tensor product.

@That_One_Guy...

4 жыл бұрын

@@evanurena8868 and your opinion is exactly why many people hate math, not every newbie is genius, they need some easier way to understand abstract things like math, things like abstract concept can just be studied later after they understand roughly what it mean.

@evanurena8868

4 жыл бұрын

@@That_One_Guy... Not every newbie may find the geometric explanation much easier then the algebraic one because those people have more trouble with spatial reasoning. What you've stated was completely irrelevant to what I said because you're making dangerous implications that don't really connect with my initial stance.

@evanurena8868

4 жыл бұрын

@Corona Kuro What do you mean by sloppy? Not everyone who isn't a traditional student watches these videos because they want to feel smart but maybe other reasons such as a genuine interest or an alternative explanation for a certain concept. The mind is a complex entity of the human body and math is an extremely broad area, so people are bound to have varying logical interpretations in how math works for them. That same person who doesn't comprehend this video on tensors is probably better adept at understanding another topic in math like differential equations or doesn't understand tensors from a geometric point of view . Whether one is in or out of school, i guess all of us in some way are students trying to learn something new one way or another.

@stephenstreet1045

3 жыл бұрын

@@evanurena8868 just ignore Corona Kuro, obviously a complete douche. I am an 'actual student' and found this video and others like a really excellent, superior in many ways to my degree text books. I used to watch things like long before I started my degree and your quite right that one doesn't need to be an 'actual student' to grapple with these topics. Universities don't hold a monopoly on learning!

5:54 the basis vectors will transform according to L inverse I don't get what you mean. Please always use examples

@manstuckinabox3679

2 жыл бұрын

Oh, well a coordinate transformation is a sort of something that transforms the coordinate system to a new one, may it be scale or angle or both, so the inverse of that transformation will return the transformed object to its original state, when we say that the basis vectors will transform according to L-1, that means once the first transformation will take place, the second one will only apply to the basis vectors, thus making the basis vectors invariant to the first transformation.

Hi, thanks for your videos!!! I think they are absolutely amazing. Could I ask you something? Could you please numerate them? I think it's kind of confusing getting to know which one is the next. Thanks. Again. Amazing videos!

@FacultyofKhan

4 жыл бұрын

Appreciate the kind words! For the numeration, it's a good idea, but I'll wait to do that until I finish the playlist; that way I can write (1/n) next to the videos, where n is the total number of videos. For now, here's a link to the playlist so you can watch everything in order: kzread.info/head/PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_

bruh how'd he write so straight without lines

Hi thx for the explanation. Can you explain why the basis vectors will transform according to L-1?

So what if the transformation law is flipped? ie. The magnitude of the components change according to L inverse, but the basis vectors change according to L? Is this a different type of tensor or does the transformation have the same effect?

When you changed the coordinates for the stress tensor. Did you change the cross sections as well?

@user-ce8rh4qk8l

Жыл бұрын

Yes, as far as I understand

I have a question. Component of tensor will transform according to L, does component mean magnitude? If yes, then if magnitude is transforming according to L and base vector(direction) Transforming according to L-1. How are they cancelling each others effect. One is magnitude the other is direction.

What does it mean for a vector to change (or remain the same)? That was not explained. And why do the components transform according to L and the bases according to L^-1?

is changing betwee cartesian and polar coordinates a tensor transformation?

Regarding your first definition, Neuenschwander made a joke about that very thing in his book in his opening chapter... Seriously, It must be some kind of hazing process by mathematicians to define tensors based on how they transform. LOL. One of those "if you don't understand it don't expect me to be obliged to explain it to you."

Can someone explain, what would be a reason you would change the coordinate system on a stress tensor?

Great

As a senior in high school, this video raped my mind, yet was extremely helpful. Overall 9.9/10

I totally appreciate the fundamental approach to teaching tensor types. However, one thing I would suggest is to use a more practical example of the beam. Affix one side of the beam to a surface, and place the O stress tensor at the other. You can then apply the concept directly, rather than leaving it up to the reader to interpret the concept in some arbitrary way. Thanks! ☺

Try to make a video on Tensor Product

@FacultyofKhan

5 жыл бұрын

In the future, I will!

Please just confirm if these dimensions, of the terms in the field equation, found on the internet, are correct or wrong. [G(miu,niu)]=M.L^-1.T^-2; [R]=[Lamda]=L^-2; [g(miu,niu)]=M.L.T^-2; [T(miu,niu)]=M^2.T^-4. And if the dimensional homogeneity of the relativistic gravity equation is checked with these dimensions of the tensors and curves in the field equation?

Thanks for the video 👍. Just one remark, matrices are not just collections of numbers, they are linear transformations.

@FacultyofKhan

5 жыл бұрын

I think it depends on what sources you look at; I've always learned it as collections/arrays of numbers (and wikipedia + a number of other sources agree), but your version is also correct (and one that wolfram mathworld happens to agree with)!

@robertbrandywine

2 жыл бұрын

From the Google dictionary: a rectangular array of quantities or expressions in rows and columns that is treated as a single entity and manipulated according to particular rules. But you don't *have* to manipulate it. Just sitting there it is the first part of the definition, only.

@shinhermit

2 жыл бұрын

@@robertbrandywine I don't rely on online dictionary definitions, but on my university classes. The term appeared in 2 domains, math and computer sciences. In none of them where matrices just collections of numbers. A random collection of numbers is just an array or a multi-dimensional array. In algebra, we were presented matrices as representing transformations. As with many notions in math, once you know that and the rules to use it, you can abstract from the fact that they represent transformations, and just apply the algebraic rules to manipulate them. Now you can *choose* to forget what they essentially are and just *consider* them as collections of number (just like you can represent a vector as just a collection of numbers), but *you* doing so does not essentially changes what a matrice is. It's like looking at a text in chinese, and saying it's just a collection of symbols. Someone would tell you it's not just that, it's a language, it has meaning and purpose. But you can choose to see it as just a series of random symbols. *Edit* : if you want to convince yourself that matrices are not simple arrays, try to find *why* their algebraic operation rules are what they are. Especially, why the multiplication of matrices is the complicated formula it is, and you'll find that it is directly derived from the composition of functions (the f°g operation). The relation of matrices with functions operations (addition, substraction, composition) will also tell you what the numbers in a matrice actually represent.

0:40 that exactly what my Math teacher says. LMAO

But, looking at the components, how di touvkniw that the tensor is the same is the components change with the transformation?

So tensors are mathematical ways to describe reality. The reality doesn't change but the numbers describing the reality changes when you have a change of co-ordinate system

HAAAAllelujah. HAAAllelujah. HALLELUJAH, HALLELUJAH, HALLELOOOoooOOOJAH! Honestly I could weep.

It seems obvious that when you change the reference (the basis) then the description (the coordinates) will also change, but reality will remain the same. It's like using a different unit for temperature or money, or like describing an object in different languages, the words will change, not the object itself, be it a thing, a vector, a tensor, or anything. That said, I still don't know what a tensor is, I just know the way it's written depends on the reference used, as anything else. I certainely missed something important in this video, but what ?

@robertbrandywine

2 жыл бұрын

I'm with you. Could it be that a tensor is an array of numbers that express some vector space values and that each point contains vectors that give the rules for correct each point values to the new coordinate system? That's probably not right.

A tensor is something that transforms like a tensor

Can you give an example of a matrix that has physical significance but is not a tensor?

@AdrianBoyko

11 ай бұрын

[23, 27, 33] where these numbers are the ages of some three people at a given point in time.

The way this guy explains tensors is the exact reason why you go through college without understanding tensors. All those bad books and pdfs start explaining tensors from some application point of view. So they tell you about tensors and what tensors do without telling you what a tensor is. This video is more about the stress tensor than a general tensor. If you want to have even a basic understand of tensors, start with a modest understanding of linear algebra, then came back and focus on basis vectors, then learn forward and backwards transformations from one basis to another. Do tons of examples till you understand forward and backward transformation from one basis to another well, then go study covectors, again do practice examples till your fingers are blistered. Then go study the tensor product. Then you will have the correct intuition and working knowledge of tensors. Do this and you will thank me later. Don't waste your years with the stress tensor, or moments of inertia, or the metric tensor etc. Come back to all these high level applications after you have a working knowledge of tensors. In fact the first application you should study after you follow my recommendation is the metric tensor. You probably could learn right now how to write the metric tensor for any surface by just deriving the first fundamental form for that surface, extracting all the components of the metric tensor and then writing out the metric tensor for the surface or space. However, that will not give you even a basic working knowledge of tensors. If you want to go higher after following my guidance, then you can start studying tensor calculus.

@nightmareshogun6517

4 жыл бұрын

Thanks for that buddy

''A tensor is an object that transforms like a tensor'', What does this mean? Does the second ''tensor'' mean an physics object which can transform something like a rubiks cube?

I have to understand tensor to implement a research paper, damn its getting a bit too much

2:50 the displacement does not change only the components do

Tensor apt regression_likely

At 6:20 , why do the basis vectors transform according to L-1 and not L ?

@tanchienhao

5 жыл бұрын

my guess (im not fully sure) is you can say that basis vectors transform under L, but then the components wld transform under -1... so perhaps its a matter of convention

@FacultyofKhan

5 жыл бұрын

@@tanchienhao You guessed correct! It's just a matter of convention; I was using it to intuitively describe how tensors would transform. The overall point is that basis vectors and components would transform in an inverse manner.

@robertbrandywine

2 жыл бұрын

@@FacultyofKhan Does inverse here mean "counter-acting"?

How do you speak such long sentences

could you plsss share this lecture in Pdf. if you are reading this comment, i would say i love you ❤.

In a few words a tensor is Aijk i©j©k. Where © is the tensorial product 😂 while the matrix representing the coordinates of the tensor is only represented by the coordinates Aijk. (Pretend the c inside the circle © is an x) 😂 That's the only thing I found on my phone.

Actually a matrix is a (1,1) tensor.

Who is Marcin Maciejewski, Kto to jest Marcin Maciejewski? Czy zna on Mateusza Macielewskiego?

**A tensor is a mathematical object that transforms like a tensor.** Hmmm yes the floor here is made out of floor

@JoseMejia-hi8zd

4 жыл бұрын

Indeed.... Is the most important fact of a tensor. I think that this sentence means that a tensor transforms in a special way, that is, this way is unique and only the tensors transforms it this way

what is the purpose of change of coordinates?

@marrytesfu3163

5 жыл бұрын

Some problems becomes easy after changing the coordinates