Intro to tensors

A basic introduction to what tensors are.

[IntegralMoon]

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

[johnholme]

Excellent introduction! The rankings are crystal clear now.

[ninosawbrzostowiecki]

I appreciate the self deprecating humor.

[mshahzaib]

Thank you so much, you explained it in simple words

[fredcsjb]

Your videos are awesome! Keep'em coming!

[lilydog]

Visually very useful in explaining tensors.

[RedTriangle]

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.

[scitwi]

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.

[jkli]

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

[samaramar]

are tensors scalars? or vectors? or neutral?

[kyrinky]

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.

[alfreds.]

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

[ifnstorm]

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 .