Annals of Mathematical Sciences and Applications
Volume 8 (2023)
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
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.
convex decomposition, row-stochastic matrix, decomposition algorithm
2010 Mathematics Subject Classification
Primary 15B51. Secondary 47L07.
Published 26 July 2023