Contractive Matrices of Hua Type

Authors

Guanghui Xu, Zhejiang Forestry University
Changqing Xu, Zhejiang Forestry University
Fuzhen Zhang, Nova Southeastern University; Shenyang Normal UniversityFollow

Document Type

Article

Publication Date

2-1-2011

Publication Title

Linear and Multilinear Algebra

Keywords

Contractions, Contractive matrices, Determinant inequalities, Eigenvalues, Elementary symmetric functions, Hua's determinant inequality, Hua's matrix inequality, Matrix inequalities, Positive semidefinite matrix

ISSN

0308-1087

Volume

59

Issue/No.

2

First Page

159

Last Page

172

Abstract

This is continuation of the recent work by Xu, Xu and Zhang [Revisiting Hua–Marcus–Bellman–Ando inequalities on contractive matrices, Linear Algebra Appl. 430 (2009), pp. 1499–1508] on contractive matrices. We study the relations of block matrices of Hua type, present some properties that the eigenvalues of Hua matrices possess, especially for the 2 × 2 block case, discuss the analogues for higher dimensions and estimate the closeness of two Hua matrices. At the end, we propose a conjecture on the eigenvalues of Hua matrices and an open problem on the symmetric functions of the eigenvalues of contractive matrices.

Comments

AMS Subject Classifications: 15A15, 15A24, 15A45

NSUWorks Citation

Xu, Guanghui; Xu, Changqing; and Zhang, Fuzhen, "Contractive Matrices of Hua Type" (2011). Mathematics Faculty Articles. 47.
https://nsuworks.nova.edu/math_facarticles/47

DOI

10.1080/03081080903266888