Root spreads for polynomials and Hermitian matrix pencils
type: Item
instance of: scholarly article
title: Root spreads for polynomials and Hermitian matrix pencils
zbMATH Open document ID: 0824.15013
DOI: 10.1016/0024-3795(94)00051-E
author: Robert C. Thompson
published in: Linear Algebra and its Applications
publication date: 1995-11-15T00:00:00Z
review text: Let \(f(x)\) be a polynomial with real roots \(x_ 1,\dots,x_ n\) and let be \(f_ i(x)\), \(i= 1,\dots, n\) be certain linear combinations of the polynomials \(f(x)/(x- x_ i)\). The spread of a polynomial is the difference of its largest and smallest root. The author compare the spreads of \(f(x)\) and of the \(f_ i(x)\). This is applied to the spreads of the eigenvalues of an Hermitian matrix and the spreads of its principal submatrices.
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 769037
zbMATH Keywords: root spreads for polynomials
zbMATH Keywords: Hermitian matrix pencils
zbMATH Keywords: spreads of the eigenvalues
zbMATH Keywords: Hermitian matrix
reviewed by: Hubert Grassmann
MaRDI profile type: Publication
cites work: On Cauchy's Inequalities for Hermitian Matrices
cites work: Numerical ranges of principal submatrices
cites work: Eigenvalue inequalities for principal submatrices
cites work: On the spread of a hermitian matrix and a conjecture of thompson
cites work: On the eigenvalues of principal submatrices of normal, hermitian and symmetric matrices
cites work: The eigenvalue spreads of a hermitian matrix and its principal submatrices
cites work: Principal submatrices. VIII: Principal sections of a pair of forms
cites work: Principal submatrices of normal and Hermitian matrices
full work available at URL: 0024-3795(94)00051-e
OpenAlex ID: W2059276620
description: scientific article; zbMATH DE number 769037