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Extreme points in convex sets of symmetric matrices


Author: Bernard Ycart
Journal: Proc. Amer. Math. Soc. 95 (1985), 607-612
MSC: Primary 15A48; Secondary 52A20
MathSciNet review: 810172
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Abstract: This paper deals with the following problem: What are the extreme points of a convex set $ K$ of $ n \times n$ matrices, which is the intersection of the set $ {S_n}$ of symmetric matrices of nonnegative type, with another convex subset of symmetric matrices $ H?$? In the case where the facial structure of $ H$ is known, we expose a general method to determine the extreme points of $ K$ (Theorem 1). Then, we apply this method to the set of correlation matrices, characterizing its extreme points in Theorem 2, which is our main theorem. A corollary describes thoroughly the extreme points of rank 2.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0810172-4
Keywords: Extreme points, correlation matrices
Article copyright: © Copyright 1985 American Mathematical Society