scholarly journals Positive definite doubly stochastic matrices and extreme points

1986 ◽  
Vol 82 ◽  
pp. 123-132 ◽  
Author(s):  
Jens Peter Reus Christensen ◽  
Pal Fischer
Keyword(s):  
Extreme Points ◽  
Positive Definite ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Doubly Stochastic Matrices

Extreme points of convex sets of doubly stochastic matrices. II

1975 ◽  
Vol 78 (2) ◽  
pp. 327-331
Author(s):  
J. G. Mauldon
Keyword(s):  
Convex Sets ◽  
Convex Set ◽  
Extreme Points ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Doubly Stochastic Matrices

We prove a conjecture of (5), namely that the convex set of all infinite doubly stochastic matrices whose entries are all strictly less than θ(0 < θ ≤ 1) possesses extreme points if and only if θ is irrational.

scholarly journals A short note on extreme points of certain polytopes

2020 ◽  
Vol 8 (1) ◽  
pp. 36-39
Author(s):  
Lei Cao ◽  
Ariana Hall ◽  
Selcuk Koyuncu
Keyword(s):  
Short Proof ◽  
Convex Polytopes ◽  
Short Note ◽  
Convex Polytope ◽  
Extreme Points ◽  
Alternative Proof ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem

AbstractWe 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.

scholarly journals Positional Voting and Doubly Stochastic Matrices

2021 ◽  
Vol 128 (4) ◽  
pp. 337-351
Author(s):  
Jacqueline Anderson ◽  
Brian Camara ◽  
John Pike
Keyword(s):  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Doubly Stochastic Matrices ◽  
Positional Voting
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