In mathematics, especially in probability and combinatorics, a doubly stochastic matrix is a square matrix X = {\displaystyle X=} of nonnegative real numbers, each of whose rows and columns sums to 1, i.e., ∑ i x i j = ∑ j x i j = 1, {\displaystyle \sum _{i}x_{ij}=\sum _{j}x_{ij}=1,} Thus, a doubly stochastic matrix is both left stochastic and right stochastic. Wikipedia