On bounds of extremal eigenvalues of irreducible and \(m\)-reducible matrices

DOI10.1016/j.laa.2004.12.004zbMath1079.15018OpenAlexW2130157567MaRDI QIDQ556873

Chai Wah Wu

Publication date: 23 June 2005

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2004.12.004

zbMATH Keywords

Markov chainsgraphsstochastic matricesdirected graphsalgebraic connectivityreducible matricesLaplacian matricesGershgorin circle criterionLevy- Desplanques theoremlocalization of eigenvalues

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48) Directed graphs (digraphs), tournaments (05C20) Stochastic matrices (15B51)

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Cites Work

• On Rayleigh-Ritz ratios of a generalized Laplacian matrix of directed graphs
• Exponential convergence of products of stochastic matrices
• Bounds for eigenvalues of doubly stochastic matrices
• Synchronization in networks of nonlinear dynamical systems coupled via a directed graph
• Matrix Analysis
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• SYNCHRONIZATION STABILITY IN COUPLED OSCILLATOR ARRAYS: SOLUTION FOR ARBITRARY CONFIGURATIONS
• A Sufficient Condition for Nonvanishing of Determinants
• Products of Indecomposable, Aperiodic, Stochastic Matrices
• A Recurring Theorem on Determinants
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