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Math Help - Homework help! Matrix determinant question?

  1. #1
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    Homework help! Matrix determinant question?

    What is wrong with the proof that projection matrices have det (P) = 1?

    P = A(AtA)^-1At

    so

    |P| = |A| (1/ (|At| |A|)) |At| = 1


    I understand that that det (AB) = |A| |B|, so what's wrong with this proof?
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  2. #2
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    If you are given that P = A(A^{T}A)^{-1}A^T, since A is not necessarily square so that det(A) is not necessarily defined, a safe tact is to show that P^2=P.
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  3. #3
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    Quote Originally Posted by Unco View Post
    a safe tact is to show that P^2=P.
    What is the only number that fits the equation?
    x=x^n
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