On the second real eigenvalue of nonegative and Z-matrices

DOI10.1016/S0024-3795(96)00033-XzbMath0874.15011MaRDI QIDQ677818

Shmuel Friedland, Reinhard Nabben

Publication date: 13 November 1997

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

zbMATH Keywords

upper boundsadjacency matrix\(Z\)-matricesnon-negative matricesmaximal spectral radiusconnected regular graphsecond real eigenvalue

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (6)

On Spectral Integral Variations of Graphs ⋮ \(Z\)-matrices and inverse \(Z\)-matrices ⋮ A note on improvement on bounds for nonmaximal eigenvalues of symmetric positive matrices ⋮ Tight estimates for convergence of some non-stationary consensus algorithms ⋮ Schur complements and its applications to symmetric nonnegative and \(Z\)-matrices ⋮ On the Perron roots of principal submatrices of co-order one of irreducible nonnegative matrices

Cites Work

• Unnamed Item
• Bounds on the spectrum of nonnegative matrices and certain Z-matrices
• The reconstruction of a symmetric matrix from the spectral data
• A classification of matrices of class Z
• Lower bounds for the first eigenvalue of certain M-matrices associated with graphs
• \(Z\)-matrices and inverse \(Z\)-matrices
• Matrix Analysis
• An Upper Bound for the Real Part of Nonmaximal Eigenvalues of Nonnegative Irreducible Matrices
• On some properties of matrices with positive elements

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