Intro to tensors

Рет қаралды 44,214

PhysicsHelps

9 жыл бұрын

A basic introduction to what tensors are.

Пікірлер: 31

@johnholme783 7 жыл бұрын

Excellent introduction! The rankings are crystal clear now.

@IntegralMoon 9 жыл бұрын

This is awesome :) I'd love to see more of these!

@fredcsjb2077 9 жыл бұрын

Your videos are awesome! Keep'em coming!

@ninosawbrzostowiecki1892 8 жыл бұрын

I appreciate the self deprecating humor.

@mshahzaib4195 7 жыл бұрын

Thank you so much, you explained it in simple words

@lilydog1000 6 жыл бұрын

Visually very useful in explaining tensors.

@mijnkampvuur 9 жыл бұрын

Good and simple explanation!

@RedTriangle53 7 жыл бұрын

To anyone who thinks the explanation was too vague, it's really supposed to be. The definition of a tensor is even vaguer. Basically an n-rank tensor is an n-dimensional grid of scalars. Each tensor has some different function, just like a temperature scalar has a different function from a probability scalar, the different tensors just tend to have more complex varieties. The jacobi matrix(spatial higher order derivative) of a velocity vector is a specific rank 2 acceleration tensor for example, but the stress tensor, also rank 2, has a very different meaning and application. The thing they have in common is that they are mathematical constructs of a certain dimension. Just like a unit vector and a force vector and a curl vector are different, but still rank 1 tensors because they are one layer deep.

@abebuckingham8198 6 жыл бұрын

Perhaps your background in physics has ill-prepared you for this but there is no mathematical vagueness in their definition. You have reduced the nature of tensors to indexing entries in an array but this is just a means of representing a tensor, it is not what a tensor actually is. The definitive property is that they are multilinear maps and you have mentioned this nowhere in your video. Your explanation is not merely vague, it's incorrect.

@jkli6031 8 жыл бұрын

Actually there are some interesting properties for those things to become what we call a 'tensor'

@samaramar2662 7 жыл бұрын

are tensors scalars? or vectors? or neutral?

@RedTriangle53 7 жыл бұрын

I don't know what you mean by neutral. Vectors and scalars are types of tensors. A tensor is basically any mathematical construct that makes sense physically, and with higher ranks you can achieve higher complexity.

@samaramar2662 7 жыл бұрын

what is a mathematical construct?

@RedTriangle53 7 жыл бұрын

It's synonymous with `mathematical object`.

@interestingmatters3-d137 7 жыл бұрын

what about space time tensors ???!??

@TheDavidlloydjones 7 жыл бұрын

I certainly am glad you raised that question, Madam. Seize, seize with both hands, with both hands I say, the opportunities as they become apparent to you, and with application, the application of your intellect to the question before you, you, you too, will in the fullness of time, be able to reach, reach I say, as so many have said before me when confronted with a question of the depth, breadth, and even more important the general applicability of the question you have so pungently brought to our attention....

@scitwi9164 7 жыл бұрын

Saying that vectors are just lists of numbers, and matrices are just arrays of numbers, is like saying that a computer is just a box with lots of buttons, and a computer program is just a string of zeros and ones. It's a true statement, but totally misses the point. Because those are just *representations* of those objects, not the objects themselves.

@samaramar2662 7 жыл бұрын

are tensors vectors? or scalars? or neutral?

@-danR 5 жыл бұрын

A vector is an _ordered_ list of numbers. I think you're getting ahead of the game and implicitly thinking about what you can _do_ with tensors, ie, "stress tensors", by which say a vector normal to a point on a surface can be related to a vector more oblique to the point that surface. But the tensor part _itself_ is still nothing but an (invariant) array of numbers.

@indranathmukherjee6164 6 жыл бұрын

But what is tensor?

@-danR 5 жыл бұрын

You mean _why_ is a tensor, ie: What good are these ordered arrays of numbers? What they _are_ could hardly have been stated more succinctly, although it would been helpful to have depicted the numbers more generally: [a b] ⎡a b⎤ ⎣c d⎦

@alfreds.3023 7 жыл бұрын

answer the "why" please. and how the are used

@kyrinky 9 жыл бұрын

It really does not help saying that you are lazy and skipping on potential good material to explain. it'd be great if you could go more into detail with this stuff, since you seem to know how to explain stuff.

@ifnstorm4158 9 жыл бұрын

Shit ! I thought matrices were at Rank 1 and vectors at Rank 2. I have to review the covariant tensor of q order by the way or I'll get confusion on tensors .