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I Transpose Property (where's my mistake)

  1. Aug 28, 2016 #1

    joshmccraney

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    Hi PF!

    When proving ##\left(AB\right)^T = B^T A^T## I was thinking of writing ##\left(AB\right)_{ij} = A_{ik} B_{kj} = D_{ij}##. Then ##\left(D\right)^T_{ij} = D_{ji} = A_{jk} B_{ki} = A^TB^T## but clearly this is incorrect. Can someone tell me where my mistake is made?

    Thanks!
     
  2. jcsd
  3. Aug 28, 2016 #2

    blue_leaf77

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    Yes, the last equality is incorrect.
    Hint: ##A_{jk}B_{ki} = (A^T)_{kj}(B^T)_{ik}##.
     
  4. Aug 29, 2016 #3

    micromass

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    You are using Einstein notation, right?
     
  5. Aug 29, 2016 #4

    joshmccraney

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    I am, and I think I found the mistake. ##A## initially had a different index, so changing that doesn't make sense, correct?
     
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