Eigenvector saddlepoints and zero properties of the eigenpolynomial factors
type: Item
instance of: scholarly article
title: Eigenvector saddlepoints and zero properties of the eigenpolynomial factors
zbMATH Open document ID: 0882.15004
DOI: 10.1016/S0024-3795(96)00292-3
author: Mark A. Mendlovitz
published in: Linear Algebra and its Applications
publication date: 1998-02-03T00:00:00Z
review text: The author establishes a number of properties of the eigenvectors of the eigenvalue problem \(Ax=\lambda Bx\), where \(A\) and \(B\) are Hermitian \((N+1)\times (N+1)\) matrices with \(B\) positive definite and, for all \(\lambda\) in some interval containing all the eigenvalues, the difference between the upper and lower \(N\times N\) principal submatrices of \(A-\lambda B\) is semidefinite. Some of the results involve polynomials whose coefficients are the components of an eigenvector.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 1044240
zbMATH Keywords: eigenvectors
zbMATH Keywords: min-max problems
zbMATH Keywords: eigenpolynomials
zbMATH Keywords: eigenvalue
reviewed by: Alan L. Andrew
MaRDI profile type: Publication
cites work: Eigenvalues and eigenvectors of symmetric centrosymmetric matrices
cites work: On the Spectra of Bounded, Hermitian, Hankel Matrices
cites work: Inertia characteristics of self-adjoint matrix polynomials
cites work: Q3993068
cites work: Q5571936
cites work: Convergence Conditions for Nonlinear Programming Algorithms
Wikidata QID: Q126340273
description: scientific article; zbMATH DE number 1044240