A is a diagonal matrix and B is a symmetric matrix, both square matrices of same order. All elements in A and B are positive. I am trying to find a formulation for the largest eigenvalue of their product, AB.
The best I can do till now is getting a bound on the largest eigenvalue of AB using the Perron-Frobenius theorem, since AB is positive. However, I am searching for a way to do better than an upper bound, if it's possible, and get an exact expression for the dominant eigenvalue.