Article
Contractive Matrices of Hua Type
Linear and Multilinear Algebra
Document Type
Article
Publication Date
2-1-2011
Keywords
- Contractions,
- Contractive matrices,
- Determinant inequalities,
- Eigenvalues,
- Elementary symmetric functions,
- Hua's determinant inequality,
- Hua's matrix inequality,
- Matrix inequalities,
- Positive semidefinite matrix
Disciplines
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.
DOI
10.1080/03081080903266888
Citation Information
Guanghui Xu, Changqing Xu and Fuzhen Zhang. "Contractive Matrices of Hua Type" Linear and Multilinear Algebra Vol. 59 Iss. 2 (2011) p. 159 - 172 ISSN: 0308-1087 Available at: http://works.bepress.com/fuzhen-zhang/35/
AMS Subject Classifications: 15A15, 15A24, 15A45