Bounds for the Perron root, singularity/nonsingularity conditions, and eigenvalue inclusion sets

DOI10.1007/s11075-006-9041-7zbMath1106.15012OpenAlexW2079131364MaRDI QIDQ857653

L. Yu. Kolotilina

Publication date: 19 December 2006

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-006-9041-7

zbMATH Keywords

spectral radiusnonnegative matricestwo-sided boundsdirected graphsdiagonal dominancePerron rooteigenvalue inclusion setsblock-partitioned matricessingularity/nonsingularity

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) Directed graphs (digraphs), tournaments (05C20)

Related Items (8)

New nonsingularity conditions for general matrices and the associated eigenvalue inclusion sets ⋮ Two inequalities for the Hadamard product of matrices ⋮ Upper and lower bounds for the Perron root of a nonnegative matrix ⋮ On the sharpness of two-sided bounds for the Perron root and of the related eigenvalue inclusion sets ⋮ A sequence of lower bounds for the spectral radius of nonnegative matrices ⋮ Some new estimations for the upper and lower bounds for the spectral radius of nonnegative matrices ⋮ New two-sided bounds for the Perron root and related nonsingularity criteria ⋮ On some inequalities for the fan product of matrices

Cites Work

• On some metrical properties of operator matrices and matrices partitioned into blocks
• A note on A. Brauer's theorem
• Bounds for the greatest characteristic root of an irreducible nonnegative matrix
• Bounds and inequalities for the Perron root of a nonnegative matrix
• Nonsingularity/singularity criteria for nonstrictly block diagonally dominant matrices.
• Generalizations of the Ostrowski-Brauer theorem
• Bounds for the greatest characteristic root of a nonnegative matrix
• Bounds and inequalities for the Perron root of a nonnegative matrix. II: Circuit bounds and inequalities
• Limits for the characteristic roots of a matrix. II
• Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices
• Matrices eigenvalues, and directed graphs
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