I've been reading about tensors recently and trying to wrap my head around the idea. I think I'm starting to get it, but it would be a big help if someone could tell me if the following ideas are correct and correct them if they are wrong:
The tensor product of two tensors V and U with ranks R and S is of rank r+s and contains every element in V times every element in U and the dimension of that tensor product is the dimensions of V for the first r indexes and the dimensions of U for the last s indexes.
A linear transformation of a tensor in a tensor space of rank r with dimensions D1..Dr to a tensor space of rank s with dimiensions E1..Es is the same rank and dimensions as the tensor product of tensors in those two spaces.
Here's is where I really get stuck:
Given a transformation T from space V to U, and a tensor field R as a function of a tensor X. How would you apply that transformation? Is it just T*R(x) or is it T*R(T*X) or is it R(T*x) or T*R(T^-1 * x) or do I need more information to transform a field than I would need to transform a regular tensor?
Any explanations, formulas, or good links would be appreciated.
This forum seems more tilted toward linear algebra than multilinear. Is there a better place to post questions about multilinear algebra, tensor calculus, etc? I have several questions, and the more I read the more questions I have. I can always ask my professors when school starts again, but I won't really have time to pursue recreational stuff when I have class....They really don't make this stuff user friendly at all...
there are a few users here who can help you with that, maybe they havent seen your question yet. you can try other math forums if you wish. you may find some in the "Useful math websites" forum. if you need links to some that come highly recommended to me from other users on this site, you can PM me
Originally Posted by Alrecenk
Ah, well I guess it hasn't even been a week yet. I'll give this a little while before I start cross posting all over the internet. I think I'll go check out the useful sites now.