A Note on Extreme Correlation Matrices
暂无分享,去创建一个
An $n\times n$ complex Hermitian or real symmetric matrix is a correlation matrix if it is positive semidefinite and all its diagonal entries equal one. The collection of all $n\times n$ correlation matrices forms a compact convex set. The extreme points of this convex set are called extreme correlation matrices. In this note, elementary techniques are used to obtain a characterization of extreme correlation matrices and a canonical form for correlation matrices. Using these results, the authors deduce most of the existing results on this topic, simplify a construction of extreme correlation matrices proposed by Grone, Pierce, and Watkins, and derive an efficient algorithm for checking extreme correlation matrices.
[1] J. Christensen,et al. A note on extreme positive definite matrices , 1979 .
[2] R. Grone,et al. Extremal correlation matrices , 1990 .
[3] R. Horn,et al. Block-matrix generalizations of Schur's basic theorems on Hadamard products , 1992 .