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Tensor property

  1. Sep 25, 2010 #1
    1. The problem statement, all variables and given/known data

    Let [tex] A_{i} , B_{j} , C_{k}[/tex]be vectors.
    Is [tex]A_{1} B_{i} + A_{2} B_{j} + A_{3} B_{k}[/tex] a tensor?

    2. Relevant equations
    [tex]T'_{ijk} = R_{il} R_{jm} R_{kn} T_{ijk} [/tex]

    3. The attempt at a solution
    If T is a tensor of rank 3, then [tex]T'_{ijk} = R_{il} R_{jm} R_{kn} T_{ijk} [/tex] where [tex] R^\intercal R =I [/tex]. But I am not sure how to use this relation in the problem. > <

    I think it is to use the property of vector [tex]A'_{i} = R_{il} A_{i} [/tex], but difficult appears when I try this way.

    Please help...
    Last edited: Sep 25, 2010
  2. jcsd
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