I have a problem in course project?
I have two positive definite $n\times n$ matrices, $A$ and $B$.
I want to find the bound of singular values of a product of these matrices ?
these matrices are unknown, and I want to solve them by bound them>
So I think I have to separate them
thanks a lot.
Any suggestion or references?

"I want to find the bound of singular values of a product of these matrices ?
these matrices are unknown, and I want to solve them by bound them"

Above: I don't understand this portion...

... are you asking if they are symmetric or semidefinite or something else?

Sorry I forget to wrote they are symmetric matrices. Best Regards

K, I'm very rusty on this :) But I did find this reference... will this help?

matrices - For what k, matrix (k A - B) is positive semidefinite? - MathOverflow (http://mathoverflow.net/questions/47630/for-what-k-matrix-k-a-b-is-positive-semidefinite)