The Extreme Points of Certain Polytopes of Doubly Substochastic Matrices

Zhi Chen; Lei Cao; Qing-Wen Wang

doi:10.1080/03081087.2019.1566431

The Extreme Points of Certain Polytopes of Doubly Substochastic Matrices

Zhi Chen
, Lei Cao
, Qing-Wen Wang

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let ω ^_π _n and ω ^t&h _n denote the convex polytope of n × n centrosymmetric doubly substochastic matrices and the convex polytope of n × n symmetric and Hankel-symmetric doubly substochastic matrices, respectively. In this paper, we investigate and fully characterize the extreme points of ω ^_π _n and ω ^t&h _n which generalizes the results by Brualdi and Cao in [Brualdi RA, Cao L. Symmetric, Hankel-symmetric, and centrosymmetric doubly stochastic matrices. ActaMath Vietnam. 2018;43:675–700].

Original language	American English
Pages (from-to)	1956-1971
Number of pages	16
Journal	Linear and Multilinear Algebra
Volume	68
Issue number	10
DOIs	https://doi.org/10.1080/03081087.2019.1566431
State	Published - Jan 21 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019 Informa UK Limited, trading as Taylor & Francis Group.

Funding

The first author is supported by the National Natural Science Foundation of China (No. 11601233); the Fundamental Research Funds for the Central Universities (No. KJQN201718); the Natural Science Foundation of Jiangsu Province (BK20160708). The third author is supported by the National Natural Science Foundation of China (No. 11571220). We are grateful to the anonymous referees for their very valuable comments on our paper.

Funders	Funder number
National Natural Science Foundation of China	11601233
Natural Science Foundation of Jiangsu Province	BK20160708, 11571220
Fundamental Research Funds for the Central Universities	KJQN201718

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Centrosymmetric matrices
Doubly substochastic matrices
Extreme points
15B51
Ravindra B. Bapat
05C50
doubly substochastic matrices
extreme points

Disciplines

Mathematics

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10.1080/03081087.2019.1566431

Cite this

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abstract = " Let ω π n and ω t\&h n denote the convex polytope of n × n centrosymmetric doubly substochastic matrices and the convex polytope of n × n symmetric and Hankel-symmetric doubly substochastic matrices, respectively. In this paper, we investigate and fully characterize the extreme points of ω π n and ω t\&h n which generalizes the results by Brualdi and Cao in [Brualdi RA, Cao L. Symmetric, Hankel-symmetric, and centrosymmetric doubly stochastic matrices. ActaMath Vietnam. 2018;43:675–700].",

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doi = "10.1080/03081087.2019.1566431",

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T1 - The Extreme Points of Certain Polytopes of Doubly Substochastic Matrices

AU - Chen, Zhi

AU - Cao, Lei

AU - Wang, Qing-Wen

PY - 2019/1/21

Y1 - 2019/1/21

N2 - Let ω π n and ω t&h n denote the convex polytope of n × n centrosymmetric doubly substochastic matrices and the convex polytope of n × n symmetric and Hankel-symmetric doubly substochastic matrices, respectively. In this paper, we investigate and fully characterize the extreme points of ω π n and ω t&h n which generalizes the results by Brualdi and Cao in [Brualdi RA, Cao L. Symmetric, Hankel-symmetric, and centrosymmetric doubly stochastic matrices. ActaMath Vietnam. 2018;43:675–700].

AB - Let ω π n and ω t&h n denote the convex polytope of n × n centrosymmetric doubly substochastic matrices and the convex polytope of n × n symmetric and Hankel-symmetric doubly substochastic matrices, respectively. In this paper, we investigate and fully characterize the extreme points of ω π n and ω t&h n which generalizes the results by Brualdi and Cao in [Brualdi RA, Cao L. Symmetric, Hankel-symmetric, and centrosymmetric doubly stochastic matrices. ActaMath Vietnam. 2018;43:675–700].

KW - Centrosymmetric matrices

KW - Doubly substochastic matrices

KW - Extreme points

KW - 15B51

KW - Ravindra B. Bapat

KW - 05C50

KW - doubly substochastic matrices

KW - extreme points

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IS - 10

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The Extreme Points of Certain Polytopes of Doubly Substochastic Matrices

Abstract

Bibliographical note

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

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