# Tensor Algebra question

• Feb 12th 2011, 05:57 PM
gamerman315
Tensor Algebra question
I am working on my homework for a class, and I am really stuck

the question I was given was:

prove that S(a ⊗ b) = (Sa) ⊗ b

Does anyone have any tips on how to solve this?

For further explanation this is problem 6a from this book on the page the link goes to

sorry I should have elaborated further. S is suppose to be a tensor map while a and b are supposed to be vectors

upon further looking at the book, it looks like a linear map. But I guess what they were just trying to get across is that it is a Tensor. such that v = Su. The hint in the back of the book says apply each side of the identity to an arbitrary vector v.
• Feb 13th 2011, 06:14 AM
zzzoak
Definition:

$\displaystyle (a \otimes b)v=(bv)a$

$\displaystyle (ST)v=S(Tv)$

$\displaystyle S(a \otimes b)v=S \: ( \: (a \otimes b)v \:)=S \: ( \: (bv)a \: )=(bv) \: Sa$

$\displaystyle ( \: (Sa )\otimes b \: ) \: v= \: (bv)Sa$
• Feb 13th 2011, 05:09 PM
gamerman315
thanks a lot that did the trick!