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Show for tensors (A · B) : C = A^T · C : B = C · B^T : A

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data
    using Einstein notation, show the following identities are true

    (A · B) : C = A^T · C : B = C · B^T : A



    2. Relevant equations



    3. The attempt at a solution
    (A · B) : C=(A_{ij} · B_{jk} ) : C
    = D_{ik} C_{ik}
    = C_{ik} D_{ik}
    = C_{ik} (A_{ij} · B_{jk} )

    That's as far as I can get. No clue as what to do next, any pointers would be
    greatly appreciated :)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 28, 2012 #2
    Bjk = BTkj
     
  4. Oct 1, 2012 #3
    Thanks for the response :)
    I got it solved since then, I had trouble trying to convert the double inner product as
    a summation. Once I figured that out, it was as easy as pie
     
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