A Short Note on Extreme Points of Certain Polytopes

Authors

Lei Cao, Nova Southeastern UniversityFollow
Ariana Hall, University of North Georgia
Selcuk Koyuncu, University of North Georgia

Document Type

Article

Publication Date

1-21-2020

Publication Title

Special Matrices

Keywords

Doubly (sub)stochastic matrices, Symmetric doubly (sub)stochastic matrices, Extreme points

ISSN

2300-7451

Volume

8

Issue/No.

1

First Page

36

Last Page

39

Abstract

We give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly substochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

Comments

©2020 Lei Cao et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution alone 4.0 License.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

NSUWorks Citation

Cao, Lei; Hall, Ariana; and Koyuncu, Selcuk, "A Short Note on Extreme Points of Certain Polytopes" (2020). Mathematics Faculty Articles. 291.
https://nsuworks.nova.edu/math_facarticles/291

DOI

10.1515/spma-2020-0005