Matrix-valued Jensen's inequality and its application to eigenvalue analysis

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Lim, Yongdo¹  Palfia, Miklos^1,2 

[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

[2] Univ Szeged, Bolyai Inst, Funct Anal Res Grp, Aradi Vertanuk Tere 1, H-6720 Szeged, Hungary

关键词: Positive definite matrix;    Jensen's inequality;    Wasserstein distance;    Contractive barycenter;    Majorization;    Eigenvalue inequalities;   

DOI  :  10.1016/j.jmaa.2018.04.072

来源: Elsevier

【 摘 要 】

We first establish Jensen's inequality for lower semicontinuous convex functions from a Hadamard space into an ordered Hadamard space. We apply Jensen's inequality to matrix valued integrable functions on probability measure spaces and provide new results on matrix analysis and eigenvalue analysis by discovering a variety of Lipschitz convex functions related to eigenvalue maps and Lowner ordering of positive definite matrices. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free