[線代] eigenvalue eigenvector & projection & reflection

[superconan (超級柯南)]

What are the eigenvalues and eigenvectors of a projection ? A reflection ?


目前我知道投影矩陣 P = A(A^TA)^(-1)A^T 且 P^2 = P

Let t is an eigenvalue of P and v is an eigenvector of P, then Pv = tv. — (1)

Pv = P^2v = P(Pv) = P(tv) = t(Pv) = t(tv) = t^2v. — (2)

By (1), (2)  =>  t^2 = t  =>  t^2 - t = 0  =>  t(t-1) = 0  =>  t = 0, 1


其他的就不知道怎麼求了

麻煩高手解惑，謝謝～

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