Question: Let A, B S n be such that 1. Show that all eigenvalues of BA are real and positive (despite the fact that BA

Let A, B ∈ Sn be such that A>0, B 0.

1. Show that all eigenvalues of BA are real and positive (despite the fact that BA is not symmetric, in general).

2.

3. With all terms defined as in the previous point, prove that

A>0, B 0.

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