On diagonals of matrices doubly stochastically similar to a given matrix Original Research Article

A complex matrix is doubly quasistochastic if all its row sums and column sums are 1. Matrices A and B are doubly stochastically similar if B = SAS−1, where S is doubly quasistochastic. We obtain a necessary and sufficient condition for a given matrix A to be doubly stochastically similar to a matrix with equal diagonal elements, and a necessary and sufficient condition for A to be doubly stochastically similar to a matrix with any diagonal elements the sum of which equals trace(A). Then an inverse elementary divisor result for doubly quasistochastic matrices is obtained.