Extreme points in convex sets of symmetric matrices
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- by Bernard Ycart PDF
- Proc. Amer. Math. Soc. 95 (1985), 607-612 Request permission
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.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 607-612
- MSC: Primary 15A48; Secondary 52A20
- DOI: https://doi.org/10.1090/S0002-9939-1985-0810172-4
- MathSciNet review: 810172