Doubly stochastic matrix
= Doubly stochastic matrix
{wiki}
A square real <matrix> is doubly stochastic if its entries are nonnegative and every row and column sums to $1$. Its positive-entry support satisfies the condition of the <Hall marriage theorem>: for a row subset $S$, $|S|\leq|N(S)|$ by summing column capacities. Consequently its support contains a <permutation matrix>.