Bound of eigenvalues of product of two positive definite matrices

Asked Aug 19 '19 at 17:40

Active Aug 19 '19 at 17:40

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Suppose I have two positive definite matrices A and B, Eigenvalues of A are bounded between u, v Eigenvalues of B are bounded between s, t All real numbers u,v,s,t are in range [0, 1].

I can infer that their multiplication (AB) is also positive definite, and also infer a bound on the eigenvalues of AB?

Thanks

asked Aug 19 '19 at 17:40

Chen Chen

1

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Can you clarify which definition of "positive definite" you're using? For instance, are positive definite matrices necessarily symmetric?
– Ben Grossmann Aug 19 '19 at 18:16

Bound of eigenvalues of product of two positive definite matrices

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