# Math Help - Tensor Algebra question

1. ## 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.

2. Definition:

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

$
(ST)v=S(Tv)
$

$
S(a \otimes b)v=S \: ( \: (a \otimes b)v \
=S \: ( \: (bv)a \: )=(bv) \: Sa
" alt="
S(a \otimes b)v=S \: ( \: (a \otimes b)v \=S \: ( \: (bv)a \: )=(bv) \: Sa
" />

$
( \: (Sa )\otimes b \: ) \: v= \: (bv)Sa
$

3. thanks a lot that did the trick!