Trace minimization principles for positive semi-definite pencils
type: Item
instance of: scholarly article
title: Trace minimization principles for positive semi-definite pencils
zbMATH Open document ID: 1262.15010
author: Xin Liang
author: Ren-Cang Li
author: Zhaojun Bai
published in: Linear Algebra and its Applications
publication date: 2013-03-05T00:00:00Z
review text: The authors, for a given (regular or singular) Hermitian matrix pencil \(A-\lambda B\) of order \(n\), are interested in when \(\inf_{X^HAX=J_k}\mathrm{trace}(X^HAX)\) is finite and attainable. First, in the introduction, they present the problem and they refer to previously established results from other authors, especially for the case of \(B\) being a non singular matrix. In the next two sections, they provide and prove their main results. Finally, in the fourth section, they prove a sufficient and necessary condition for infimum attainability.
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 6141612
zbMATH Keywords: Hermitian matrix pencil
zbMATH Keywords: positive semi-definite
zbMATH Keywords: trace minimization
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvector
zbMATH Keywords: Hermitian matrix
reviewed by: Ioannis K. Dassios
MaRDI profile type: Publication
full work available at URL: j.laa.2012.12.003
OpenAlex ID: W2057524212
cites work: Matrix Analysis
cites work: Q3998482
cites work: A Trace Minimization Algorithm for the Generalized Eigenvalue Problem
cites work: Trace minimization and definiteness of symmetric pencils
cites work: Q5711210
cites work: A variational principle for eigenvalues of pencils of Hermitian matrices
cites work: Variational principles for indefinite eigenvalue problems
cites work: Q3831133
cites work: A minimax characterization for eigenvalues of Hermitian pencils
cites work: A minimax characterization for eigenvalues of Hermitian pencils. II
cites work: On perturbations of matrix pencils with real spectra, a revisit
cites work: Perturbation bounds for the definite generalized eigenvalue problem
cites work: A note on Stewart's theorem for definite matrix pairs
cites work: The perturbation bounds for eigenspaces of a definite matrix-pair
DOI: 10.1016/J.LAA.2012.12.003
description: scientific article; zbMATH DE number 6141612