I would like to get your help with this problem.
Suppose $A$ is an $n$ by $n$ irreducible nonnegative matrix and $D$ is a nonnegative diagonal matrix. Both $A$ and $D$ real. Suppose the spectral radius of $DA$ (that is $\rho(DA)$ ) is a convex function on the space of nonnegative diagonal matrices.
I would like to compute the gradient of $\rho(DA)$ at $D_1$, where $D_1$ is in the space of nonnegative diagonal matrices.
thank you and hoping to get a quick reply
