Faces of the polytope of doubly substochastic matrices

Authors

Lei Cao, Nova Southeastern UniversityFollow
Zhi Chen, Nanjing Agricultural University

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 w_n. 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 w_n . Moreover, we explore the relation between the faces of w_n and the faces of Ω_n, the convex polytope of all n x n doubly stochastic matrices.

Comments

MSC

NSUWorks Citation

Cao, Lei and Chen, Zhi, "Faces of the polytope of doubly substochastic matrices" (2022). Mathematics Faculty Articles. 341.
https://nsuworks.nova.edu/math_facarticles/341

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1016/j.laa.2021.11.012