Invertibility of irreducible matrices
type: Item
instance of: scholarly article
title: Invertibility of irreducible matrices
zbMATH Open document ID: 0886.15026
DOI: 10.1016/S0024-3795(96)00241-8
author: Bit-Shun Tam
author: Shangjun Yang
author: Xiao-Dong Zhang
published in: Linear Algebra and its Applications
publication date: 1998-04-23T00:00:00Z
review text: This paper is in part survey and in part research. The topics are invertibility conditions for irreducible matrices. Classical results such as Gershgorin's circles, Cassini's ovals, Brualdi's cycle theorem, Taussky's relaxation theorem and others are analyzed and extended to cover multibounds. There are new results on eigenvalues and corresponding eigenvectors on the boundary of several of the above spectral inclusion regions, as well as extensions of \textit{V. N. Solovev}'s generalization of Gershgorin's theorem [Izv. Akad. Nauk SSSR, Ser. Mat. 47, No. 6, 1285-1302 (1983; Zbl 0551.65017)] on the invertibility of matrices.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1044226
zbMATH Keywords: irreducible matrix
zbMATH Keywords: invertibility
zbMATH Keywords: eigenvalue
zbMATH Keywords: spectral inclusion
zbMATH Keywords: Gershgorin's circles
zbMATH Keywords: Cassini's ovals
zbMATH Keywords: Brualdi's cycle theorem
zbMATH Keywords: Taussky's relaxation theorem
zbMATH Keywords: eigenvectors
reviewed by: Frank Uhlig
MaRDI profile type: Publication
cites work: Bounds for determinants
cites work: Q3943082
cites work: Limits for the characteristic roots of a matrix. II
cites work: Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices
cites work: Limits for the characteristic roots of a matrix. V
cites work: Matrices eigenvalues, and directed graphs
cites work: Combinatorial matrix theory
cites work: The symbiotic relationship of combinatorics and matrix theory
cites work: Regions in the Complex Plane Containing the Eigenvalues of a Matrix
cites work: Minimal G-functions
cites work: On collections of G-functions
cites work: Minimal Geršgorin sets and ω-matrices
cites work: Note on circular disks containing the eigenvalues of a matrix
cites work: Criteria for invertibility of diagonally dominant matrices
cites work: Patterns of Dependence in Generalizations of Gerschgorin’s Theorem
cites work: Matrix Analysis
cites work: A counterexample connected with Geršgorin's theorem
cites work: Bounds for Determinants with Dominant Principal Diagonal
cites work: Some sufficient conditions for the non-degeneracy of matrices
cites work: A GENERALIZATION OF GERSHGORIN'S THEOREM
cites work: A Recurring Theorem on Determinants
cites work: High, low, and quantitative roads in linear algebra
cites work: Minimal Gerschgorin sets
cites work: On recurring theorems on diagonal dominance
cites work: A note on A. Brauer's theorem
cites work: Q4211290
description: scientific article; zbMATH DE number 1044226