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# Annals of Mathematical Sciences and Applications

## Volume 8 (2023)

### Number 2

### Special issue dedicated to Anthony To-Ming Lau on his 80th birthday

Guest Editors: Xiaolong Qin, Ngai-Ching Wong and Jen-Chih Yao

### The convex decomposition of row-stochastic matrices

Pages: 289 – 306

DOI: https://dx.doi.org/10.4310/AMSA.2023.v8.n2.a5

#### Authors

#### 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.

#### Keywords

convex decomposition, row-stochastic matrix, decomposition algorithm

#### 2010 Mathematics Subject Classification

Primary 15B51. Secondary 47L07.

Published 26 July 2023