A counterexample connected with Geršgorin's theorem
type: Item
instance of: scholarly article
title: A counterexample connected with Geršgorin's theorem
zbMATH Open document ID: 0803.15017
DOI: 10.1016/0024-3795(94)90113-9
author: Morris Newman
author: Robert C. Thompson
published in: Linear Algebra and its Applications
publication date: 1994-08-15T00:00:00Z
review text: Let \(A=(a_{ij})\) be an \(n \times n\) complex matrix. It is known that a union of disks in the complex plane contains all eigenvalues of \(A\). In this classical Gershgorin theorem each disk has its center at a single diagonal element \(a_{ii}\) of \(A\). \textit{A. Brauer}'s generalization [Duke Math. J. 14, 21-26 (1947; Zbl 0029.33701)] of Gershgorin's theorem provides a second order union. In this note the authors exhibit examples demonstrating that a third order Gershgorin region need not contain any eigenvalue.
reviewed by: K.Burian
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 614179
zbMATH Keywords: counterexample
zbMATH Keywords: complex matrix
zbMATH Keywords: eigenvalues
zbMATH Keywords: Gershgorin's theorem
zbMATH Keywords: Gershgorin region
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90113-9
OpenAlex ID: W2063249840
Wikidata QID: Q125040902
cites work: Limits for the characteristic roots of a matrix. II
cites work: Matrices eigenvalues, and directed graphs
cites work: Q5659694
cites work: High, low, and quantitative roads in linear algebra
description: scientific article; zbMATH DE number 614179