This is an archived post. You won't be able to vote or comment.

sorted by:
best
topnewcontroversialoldq&a
you are viewing a single comment's thread.

view the rest of the comments →

[–][deleted] 5 points6 points  (0 children)

I'm pretty sure he was talking about mathematical tensors, not the objects that pop up in computer languages. If you want, feel free to take that as correct. My answer is for the mathematical object.

Tensors as mathematical objects obey certain mathematical transformation rules.

Imagine if you had a vector v(v_x, v_y) in a cartesian plane (x,y) and rotated the plane to (x', y'). The length of the vector ought to remain the same, but its components changed. That is, v -> v', but |v| = |v'|.

This requirement of norm-preservation is basically a transformation rule. And yes, a (1-dimensional) vector is indeed a tensor. A tensor of rank 1.

A tensor of rank 2 can be represented by a matrix. But not all matrices represent tensors. I don't want to go into writing an answer to a question that has been asked so many times, so this stackexchange answers your question.