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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If you are given that $\displaystyle P = A(A^{T}A)^{-1}A^T$, since A is not necessarily square so that det(A) is not necessarily defined, a safe tact is to show that $\displaystyle P^2=P$.
Originally Posted by Unco a safe tact is to show that $\displaystyle P^2=P$. What is the only number that fits the equation? $\displaystyle x=x^n$
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