A short note on extreme points of certain polytopes

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2020-01-01 DOI:10.1515/spma-2020-0005

Lei Cao, Ariana Hall, S. Koyuncu

引用次数: 0

Abstract

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 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.

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关于某些多面体的极值点的简短注释

摘要利用Birkhoff定理和二重子随机矩阵的二重随机完备，给出了关于二重子随机阵凸多面体极值点的Mirsky结果的简短证明。此外，我们还通过其相应的环图给出了对称双亚稳定矩阵凸多面体极值点的另一个证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.