A short note on extreme points of certain polytopes

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 sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex p...

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Main Authors:	Cao Lei, Hall Ariana, Koyuncu Selcuk
Format:	Article
Language:	English
Published:	De Gruyter 2020-01-01
Series:	Special Matrices
Subjects:	doubly (sub)stochastic matrices symmetric doubly (sub)stochastic matrices extreme points 15a51 15a83
Online Access:	https://doi.org/10.1515/spma-2020-0005

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spelling	doaj-e4255e18e3e24c14ad6beb210689efdd2021-10-02T19:10:40ZengDe GruyterSpecial Matrices2300-74512020-01-0181363910.1515/spma-2020-0005spma-2020-0005A short note on extreme points of certain polytopesCao Lei0Hall Ariana1Koyuncu Selcuk2Department of Mathematics, Nova Southeastern UniversityDepartment of Mathematics, University of North GeorgiaDepartment of Mathematics, University of North GeorgiaWe 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 sub-stochastic 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.https://doi.org/10.1515/spma-2020-0005doubly (sub)stochastic matricessymmetric doubly (sub)stochastic matricesextreme points15a5115a83
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Cao Lei Hall Ariana Koyuncu Selcuk
spellingShingle	Cao Lei Hall Ariana Koyuncu Selcuk A short note on extreme points of certain polytopes Special Matrices doubly (sub)stochastic matrices symmetric doubly (sub)stochastic matrices extreme points 15a51 15a83
author_facet	Cao Lei Hall Ariana Koyuncu Selcuk
author_sort	Cao Lei
title	A short note on extreme points of certain polytopes
title_short	A short note on extreme points of certain polytopes
title_full	A short note on extreme points of certain polytopes
title_fullStr	A short note on extreme points of certain polytopes
title_full_unstemmed	A short note on extreme points of certain polytopes
title_sort	short note on extreme points of certain polytopes
publisher	De Gruyter
series	Special Matrices
issn	2300-7451
publishDate	2020-01-01
description	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 sub-stochastic 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.
topic	doubly (sub)stochastic matrices symmetric doubly (sub)stochastic matrices extreme points 15a51 15a83
url	https://doi.org/10.1515/spma-2020-0005
work_keys_str_mv	AT caolei ashortnoteonextremepointsofcertainpolytopes AT hallariana ashortnoteonextremepointsofcertainpolytopes AT koyuncuselcuk ashortnoteonextremepointsofcertainpolytopes AT caolei shortnoteonextremepointsofcertainpolytopes AT hallariana shortnoteonextremepointsofcertainpolytopes AT koyuncuselcuk shortnoteonextremepointsofcertainpolytopes
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A short note on extreme points of certain polytopes

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