Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897773 | Linear Algebra and its Applications | 2018 | 16 Pages |
Abstract
In this paper we show that the eigenvalue map and the symplectic eigenvalue map of positive definite matrices are Lipschitz for the Cartan-Hadamard Riemannian metric, and establish log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter of integrable probability Borel measures. This leads a version of Jensen's inequality for geometric integrals of matrix-valued integrable random variables.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Fumio Hiai, Yongdo Lim,