A simplified Brauer's theorem on matrix eigenvalues
type: Item
instance of: scholarly article
title: A simplified Brauer's theorem on matrix eigenvalues
zbMATH Open document ID: 0935.15018
author: Luoluo Li
published in: Applied Mathematics. Series B (English Edition)
publication date: 2000-05-09T00:00:00Z
review text: The spectrum inclusion region \(\widetilde\Omega\) of matrix eigenvalues is determined. It is simpler and tighter than those in Brauer's theorem and in \textit{X. Zhang} and \textit{D. Gu}'s work [Linear Algebra Appl. 196, 163-174 (1994; Zbl 0801.15016)]. All eigenvalues of the matrix are contained in \[ \widetilde\Omega= \bigcup_{a_{ij}\neq 0,i\neq j}\{z\in\mathbb{C}:|z-a_{ii}||z-a_{jj} |\leq r_ir_j\}. \] The number of ovals in Brauer's theorem is reduced in many cases. Eigenvalues and eigenvectors that are in the boundary of \(\widetilde\Omega\) are discussed.
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1367956
zbMATH Keywords: spectrum inclusion region
zbMATH Keywords: eigenvalues
zbMATH Keywords: eigenvectors
MaRDI profile type: Publication
full work available at URL: s11766-999-0034-x
OpenAlex ID: W2056486579
cites work: Matrix Analysis
cites work: Q5543004
cites work: A note on A. Brauer's theorem
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cites work: Invertibility of irreducible matrices
cites work: High, low, and quantitative roads in linear algebra
DOI: 10.1007/S11766-999-0034-X
description: scientific article; zbMATH DE number 1367956