Bounds for characteristic values of entire matrix pencils
type: Item
instance of: scholarly article
title: Bounds for characteristic values of entire matrix pencils
zbMATH Open document ID: 1065.15013
published in: Linear Algebra and its Applications
publication date: 2004-11-18T00:00:00Z
review text: For an infinite set of \(n\) by \(n\) matrices \(\{A_k\}\) with \(A_0=I_n\), the author studies the entire matrix pencil \(f(z) = \sum_{k=0}^\infty \;\frac{z^k}{(k!)^{^\gamma}}\;A_k\) for complex \(z\) and \(\gamma > 0\). The characteristic values of \(f\) are defined as the zeros of \(\det(f(z))\). If there are infinitely many characteristic values for \(f\) and the given set of matrices, the author gives an upper bound for the sum of reciprocals (in absolute value) of the characteristic values and upper and lower bounds for the smallest characteristic value of \(f\).
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 2116539
zbMATH Keywords: matrix pencil
zbMATH Keywords: entire matrix function
zbMATH Keywords: characteristic value
zbMATH Keywords: upper and lower bounds
author: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: j.laa.2004.04.029
OpenAlex ID: W1998539990
cites work: Q3254327
cites work: Inequalities for zeros of entire functions
cites work: Operator functions and localization of spectra
cites work: Q5571194
cites work: Q3939931
cites work: Nonlinear time-discrete systems. A general approach by nonlinear superposition
cites work: Stability of invariant subspaces of regular matrix pencils
cites work: Bounds for eigenvalues of matrix polynomials
cites work: Q3137918
cites work: Q4896037
cites work: An introduction to operator polynomials
cites work: Q3998482
DOI: 10.1016/J.LAA.2004.04.029
description: scientific article; zbMATH DE number 2116539