Some Inequalities for Sum and Product of Positive Semidefinite Matrices

Authors

Bo-Ying Wang, Beijing Normal University
Bo-Yan Xi, Beijing Normal University
Fuzhen Zhang, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

5-15-1999

Publication Title

Linear Algebra and its Applications

Keywords

Majorization, Eigenvalue, Singular value, Unitarily invariant norm, Inequality, Moore-Penrose inverse, Positive semidefinite matrix

ISSN

0024-3795

Volume

293

Issue/No.

1-3

First Page

39

Last Page

49

Abstract

The purpose of this paper is to present some inequalities on majorization, unitarily invariant norm, trace, and eigenvalue for sum and product of positive semidefinite (Hermitian) matrices. Some open questions proposed by Marshall and Olkin are resolved.

Comments

Under an Elsevier user license

MSC

• 15A09;
• 15A42

NSUWorks Citation

Wang, Bo-Ying; Xi, Bo-Yan; and Zhang, Fuzhen, "Some Inequalities for Sum and Product of Positive Semidefinite Matrices" (1999). Mathematics Faculty Articles. 110.
https://nsuworks.nova.edu/math_facarticles/110

DOI

10.1016/S0024-3795(99)00013-0