Extremal correlation matrices (Q915822)

This paper is concerned with the convex, compact set of correlation matrices, i.e. the set of positive semidefinite Hermitian matrices with main-diagonal entries equal to 1. The authors concentrate on the real case and determine the possible ranks of extreme points in this set. The principle result obtained is that the set of n-by-n correlation matrices contains extreme points of rank k if and only if \(k(k+1)\leq 2n\).