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Tensor product demonstration

  1. Apr 11, 2012 #1
    I have to demonstrate that if [tex]A^{rs}[/tex] is an antisymmetric tensor, and [tex]B_{rs}[/tex] is a symmetric tensor, then the product:
    [tex]A^{rs}B_{rs}=0[/tex]

    So I called the product:
    [tex]C^{rs}_{rs}=A^{rs}B_{rs}=-A^{sr}B_{sr}=-C^{rs}_{rs}[/tex]
    In the las stem I've changed the indexes, because it doesn't matters which is which, but I'm not sure this is fine (because I think r and s could have have associated differents values in the sum).

    Then
    [tex]2C^{rs}_{rs}=2A^{rs}B_{rs}=0[/tex]
    Is this ok?
     
  2. jcsd
  3. Apr 11, 2012 #2
    interchanging and relabeling an implied double summation is okay.
     
  4. Apr 11, 2012 #3
    Thank you xaos :)
     
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