Doubly stochastic matrix

Summary

A doubly stochastic matrix is a square nonnegative matrix in which every row and every column sums to $1$. Permutation matrices are doubly stochastic, and by the Birkhoff–von Neumann theorem every doubly stochastic matrix is a convex combination of them. These matrices describe averaging processes and appear in majorization, assignment problems and Markov chains with a uniform stationary distribution.