A Short Note on Extreme Points of Certain Polytopes

  • Lei Cao
  • , Ariana Hall
  • , Selcuk Koyuncu

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
Pages (from-to)36-39
Number of pages4
JournalSpecial Matrices
Volume8
Issue number1
DOIs
StatePublished - Jan 21 2020

Bibliographical note

Publisher Copyright:
© 2020 Lei Cao et al., published by De Gruyter 2020.

ASJC Scopus Subject Areas

  • Algebra and Number Theory
  • Geometry and Topology

Keywords

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

Disciplines

  • Mathematics

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