Simplicial Faces of the Set of Correlation Matrices.

This paper concerns the facial geometry of the set of n×n<inline-graphic></inline-graphic> correlation matrices. The main result states that almost every set of r vertices generates a simplicial face, provided that r≤cn<inline-graphic></inline-graphic>, where c<inline-graphic></inline-graphic> is an absolute constant. This bound is qualitatively sharp because the set of correlation matrices has no simplicial face generated by more than 2n<inline-graphic></inline-graphic> vertices. [ABSTRACT FROM AUTHOR]