The convex decomposition of row-stochastic matrices
Volume 8, Issue 2 (2023), pp. 289–306
Pub. online: 26 July 2023
Type: Article
Published
26 July 2023
26 July 2023
Abstract
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.