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Hence if λ ≠ 0 λ ≠ 0 is an eigenvalue of AB A B with eigenvector v v, then λ λ is an eigenvalue of BA B A with eigenvector Bv B v. Take A =XT A = X T, B = X B = X. Note that if X =[1 0] X = [ 1 0], then XTX = 1 X T X = 1 has exactly one eigenvalue at 1 1, but XXT X X T has eigenvalues {0, 1} { 0, 1 }. Share. Cite. edited Apr 26, 2013 at ...}}

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2 Answers. Sorted by: 4. If Q = xxH, then Qx = xxHx. Set λ =xHx; this means x is an eigenvector of Q relative to λ (the unique non zero eigenvalue). On the other hand, if Q is …
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