the eigenvalues of product of matrices

Asked Mar 28 '13 at 14:30

Active Mar 28 '13 at 14:30

Viewed 301 times

Let $A$ be an invertible matrix with positive eigenvalues and $B$ be a positive definite matrix . How to estimate the minimum eigenvalues of $AB$ by using the eigenvalues of $A$ and $B$. More precisely, are there some inequalities such as $\min\{\lambda(AB)\}\geq\min\{\lambda(A),\lambda(B)\}$? Here $\lambda(A)$ denotes the eigenvalue of $A$. Thank you.

asked Mar 28 '13 at 14:30

jany

Posted also at http://mathoverflow.net/questions/125836/the-eigenvalues-of-product-of-matrices – abatkai Mar 28 '13 at 16:56
So you see the sidebar entitled "Related" on the right? The first question it lists seems relevant. – user1551 Mar 28 '13 at 17:33

the eigenvalues of product of matrices

0 Answers0