Annals of Mathematical Sciences and Applications

We prove that every $m \times n$ row-stochastic (RS) matrix can be written as a convex combination of $n^m$ many $\lbrace 0, 1 \rbrace$–RS matrices. In the special cases of $2 \times 3$ and $3 \times 3$ RS matrices, the proofs are given constructively. Algorithms for computing the convex decompositions of row-stochastic matrices are provided.