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Showing T_ij*S_ij is pseudoscalar

  1. Oct 12, 2016 #1
    1. The problem statement, all variables and given/known data
    If Tij is a tensor of rank two and Sij is a pseudotensor of rank two, show that the numbers TijSik transform as a pseudotensor of rank two, and that TijSij is a pseudoscalar.

    2. Relevant equations


    3. The attempt at a solution
    I've got the transformation T'ijS'ik as a pesudotensor of rank two, since taking the product of T and S in their respective transformation form results in a solution which consists of product of |S|, two transformation matrix and product of T and S with a common index, calling it matrix R.

    In the second part, I used the result I got from the first part and changed the index k into j, giving a kronecker delta and resulting in |S|Rbb (any index suffice) where Rbb is a scalar.

    I was wondering, is showing T'ijS'ij is a pseudoscalar≡TijSij is a pseudoscalar? Do tensors hold the if and only if property?

    Thanks
     
  2. jcsd
  3. Oct 17, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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