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Math Help - Tensor Algebra question

  1. #1
    Newbie
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    Feb 2011
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    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.
    Last edited by gamerman315; February 12th 2011 at 11:50 PM.
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  2. #2
    Senior Member
    Joined
    Mar 2010
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    Definition:

    <br />
(a \otimes b)v=(bv)a<br />

    <br />
(ST)v=S(Tv)<br />


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

    <br />
( \: (Sa )\otimes b \: ) \: v= \: (bv)Sa <br />
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  3. #3
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    thanks a lot that did the trick!
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