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

Huai-Xin Cao (School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, China)

Hong-Yi Chen (Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan)

Zhi-Hua Guo (School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, China)

Tsung-Lin Lee (Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan)

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.

Full Text (PDF format)

Published 26 July 2023