Doubly (sub)stochastic matrices, Symmetric doubly (sub)stochastic matrices, Extreme points
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.
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Cao, Lei; Hall, Ariana; and Koyuncu, Selcuk, "A Short Note on Extreme Points of Certain Polytopes" (2020). Mathematics Faculty Articles. 291.