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Commutative multiplication

  1. Sep 12, 2009 #1
    1. The problem statement, all variables and given/known data

    I am trying to prove an identity and in order to finish the proof i need to show that:
    for z a p-dimensional vector and A a non-singular square (pXp) matrix - also note that T is transpose - :
    zTA^(-1)z = zzTA^(-1), where -1 denotes the inverse

    I have looked everywhere to find vector multiplication that commutes but so far can't find a rule...

    Thanks for your help!
  2. jcsd
  3. Sep 12, 2009 #2


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    That doesn't look right to me...[itex]z^TA^{-1}z[/itex] is a scalar (assuming [itex]z[/itex] is a column vector), while [itex]zz^TA^{-1}[/itex] is a [itex]p\times p[/itex] matrix.....what was the original problem?
  4. Sep 13, 2009 #3
    Hey Gabby - thank you for pointing that out (i can't believe i didnt see that!).

    I will try it again now - maybe I have done some stupid mistake.
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