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Math Help - orthogonal matrices help

  1. #1
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    orthogonal matrices help

    using the definition of an orthogonal matrix prove :
    P is an orthogonal matrix if and only if P^t is an orthogonal matrix.

    I know P is orthogonal if we can multiply P by P^t and get the identity matrix but dont know where to go from there!!
    any help appreciated!!
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by eleahy View Post
    using the definition of an orthogonal matrix prove :
    P is an orthogonal matrix if and only if P^t is an orthogonal matrix.

    I know P is orthogonal if we can multiply P by P^t and get the identity matrix but dont know where to go from there!!
    any help appreciated!!
    Just use the fact that \left(P^{\top}\right)^{-1}=\left(P^{-1}\right)^{-1}=P and so \left(P^{\top}\right)^{-1}=P=\left(P^{\top}\right)^{\top}.
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  3. #3
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    still not exactly sure but have stuff to work with ill figure it thanks so much
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