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Math Help - Proof involving transpose

  1. #1
    Newbie madmartigano's Avatar
    Joined
    Mar 2009
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    Merced, California
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    Proof involving transpose

    Prove: If {A^T}A = A, then A is symmetric & A = {A^2}

    I figured out how to prove A is symmetric:

    {({A^T}A)^T} = {A^T}{({A^T})^T} = {A^T}A

    But how do I show that A = {A^2} ?
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  2. #2
    Senior Member
    Joined
    Nov 2008
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    Paris
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    354
    Hi

    Haha, I started trying different computations using A=A^TA before realizing it is completly trivial since A is symmetric.

    So, what does A is symmetric mean for its transpose?
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