Reposting from math.sx due to lack of response. Let $A$ be a $N\times N$ positive matrix such that $A_{ij}>0$. By perron-frobenius theorem, there is a unique positive unique left eigenvector called perron vector $x$ corresponding to the largest eigenvalue and also it sums to 1. Call it as $x$. Let $D$ be a diagonal matrix such that $B=DA$ is a stochastic matrix with rows summing to 1. Call the perron vector of $B$ as $y$. How are $x$ and $y$ related?