Mathematics Faculty Articles

Title

Faces of the polytope of doubly substochastic matrices

Document Type

Article

Publication Date

3-15-2022

Publication Title

Linear Algebra and its Applications

Keywords

Faces, Facets, Doubly stochastic matrices, Doubly substochastic matrices

ISSN

0024-3795

Volume

637

First Page

59

Last Page

81

Abstract

We study the faces of the convex polytope of all n x n doubly substochastic matrices, denoted by wn. We give the necessary and sufficient conditions of a face being nonempty. We also describe all 1-dimensional faces, 2-dimensional faces, and facets of wn . Moreover, we explore the relation between the faces of wn and the faces of Ωn, the convex polytope of all n x n doubly stochastic matrices.

Comments

MSC

15B51 52B05 05A18

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1016/j.laa.2021.11.012

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