Faces of the polytope of doubly substochastic matrices
type: Item
instance of: scholarly article
title: Faces of the polytope of doubly substochastic matrices
zbMATH Open document ID: 1492.15020
author: Lei Cao
author: Zhi Chen
published in: Linear Algebra and its Applications
publication date: 2022-01-24T00:00:00Z
review text: A doubly substochastic matrix is a square nonnegative matrix such that each row and each column sums at most one. The set of all \(n\times n\) doubly substochastic matrices forms a convex polytope \(\omega_{n}\) of dimension \(n^{2}\). The paper provides necessary and sufficient conditions for a face of \(\omega_{n}\) to be nonempty, and descriptions of all 1-dimensional faces, 2-dimensional faces, and facets of \(\omega_{n}\). It is worth to recall that \textit{R. A. Brualdi} and \textit{P. M. Gibson} [J. Comb. Theory, Ser. A 22, 194--230 (1977; Zbl 0355.15013)] characterised the faces of the polytope obtained from the set of all \(n\times n\) doubly stochastic matrix, square nonnegative matrices such that each row and each column sums to one.
reviewed by: Guillermo Pineda-Villavicencio
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 05A18
zbMATH DE Number: 7462788
zbMATH Keywords: faces
zbMATH Keywords: facets
zbMATH Keywords: doubly stochastic matrices
zbMATH Keywords: doubly substochastic matrices
MaRDI profile type: Publication
full work available at URL: j.laa.2021.11.012
OpenAlex ID: W4200267740
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DOI: 10.1016/J.LAA.2021.11.012
description: scientific article; zbMATH DE number 7462788