Extreme points in convex sets of symmetric matrices

Abstract

This paper deals with the following problem: What are the extreme points of a convex set K K of n × n n \times n matrices, which is the intersection of the set S n {S_n} of symmetric matrices of nonnegative type, with another convex subset of symmetric matrices H ? H? ? In the case where the facial structure of H H is known, we expose a general method to determine the extreme points of K 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.