A stronger version of matrix convexity as applied to functions of Hermitian matrices

Abstract

A stronger version of matrix convexity, called hyperconvexity is introduced. It is shown that the function is hyperconvex on the set of Hermitian matrices and is hyperconvex on the set of positive definite Hermitian matrices. The new concept makes it possible to consider weighted averages of matrices of different orders. Proofs use properties of the Fisher information matrix, a fundamental concept of mathematical statistics.

Keywords

• Matrix convexity
• Hyperconvexity
• Fisher information