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 language | American English |
|---|---|
| Pages (from-to) | 36-39 |
| Number of pages | 4 |
| Journal | Special Matrices |
| Volume | 8 |
| Issue number | 1 |
| DOIs | |
| State | Published - 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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