On the sharpness of two-sided bounds for the Perron root and of the related eigenvalue inclusion sets

DOI10.1016/j.laa.2007.06.006zbMath1176.15024OpenAlexW2166142625MaRDI QIDQ952043

L. Yu. Kolotilina

Publication date: 6 November 2008

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

Full work available at URL: https://doi.org/10.1016/j.laa.2007.06.006

zbMATH Keywords

Perron rootPerron-Frobenius theoremeigenvalue inclusion setsCassini ovalsirreducible nonnegative matricesGershgorin theoremBrualdi inclusion theoremOstrowski-Brauer inclusion theoremsharpness of boundssimple circuits

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48)

Cites Work

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• Bounds for the Perron root, singularity/nonsingularity conditions, and eigenvalue inclusion sets
• On Geršgorin-type problems and ovals of cassini
• Bounds and inequalities for the Perron root of a nonnegative matrix
• Generalizations of the Ostrowski-Brauer theorem
• Bounds for the Perron root of a nonnegative matrix involving the properties of its graph
• 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
• Matrices eigenvalues, and directed graphs
• Geršgorin-type eigenvalue inclusion theorems and their sharpness

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