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Selected Works of Lei Cao
Article
A Short Note on Extreme Points of Certain Polytopes
Special Matrices
  • Lei Cao, Nova Southeastern University
  • Ariana Hall, University of North Georgia
  • Selcuk Koyuncu, University of North Georgia
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Document Type
Article
Publication Date
1-21-2020
Keywords
  • Doubly (sub)stochastic matrices,
  • Symmetric doubly (sub)stochastic matrices,
  • Extreme points
Disciplines
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.

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©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
Creative Commons Attribution 4.0 International
DOI
10.1515/spma-2020-0005
Citation Information
Lei Cao, Ariana Hall and Selcuk Koyuncu. "A Short Note on Extreme Points of Certain Polytopes" Special Matrices Vol. 8 Iss. 1 (2020) p. 36 - 39 ISSN: 2300-7451
Available at: http://works.bepress.com/lei-cao/28/