推 xu3g4m4 : 謝謝 12/11 00:50
※ 引述《xu3g4m4 (Lsy)》之銘言：
: Let w in C^n be a column n-vector.
: Let A=ww*
: 如何證明
: 1. w*w is an eigenvalue of A with eigenvector w.
Aw = ww*w = (w*w)w
=> w*w is an eigenvalue of A with eigenvector w
: 2. 0 is an eigenvalue of A and that any vector in the orthogonal complement of
: span(w) is an associated eigenvector.
For any vector v such that v*w = 0,
w*v = 0 and Av = ww*v = 0w = 0v
=> 0 is an eigenvalue of A and that any vector in the orthogonal complement
of span(w) is an associated eigenvector.
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