Journal of Inequalities and Applications
Volume 3 (1999), Issue 2, Pages 143-152
doi:10.1155/S1025583499000107
Abstract
A stronger version of matrix convexity, called hyperconvexity is introduced. It is shown that the function A2 is hyperconvex on the set of Hermitian matrices A and A−1 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.