On the Perron roots of principal submatrices of co-order one of irreducible nonnegative matrices

DOI10.1016/S0024-3795(02)00492-5zbMath1018.15019OpenAlexW1994956140MaRDI QIDQ1863561

Sergey V. Savchenko

Publication date: 11 March 2003

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(02)00492-5

zbMATH Keywords

nonnegative irreducible matrixPerron root spectral radius

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items

Principal submatrices of co-order one with the biggest Perron root, Rank two perturbations of matrices and operators and operator model for \(\mathbf{t}\)-transformation of probability measures, Normal matrices and their principal submatrices of co-order one, Learning and selfconfirming equilibria in network games, Eigenvalues of rank one perturbations of unstructured matrices, On the change of the Jordan form under the transition from the adjacency matrix of a vertex-transitive digraph to its principal submatrix of co-order one, On the distance to singularity via low rank perturbations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the second real eigenvalue of nonegative and Z-matrices
• An algebraic-analytic approach to nonnegative bases
• The influence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: a survey
• On the generalized nullspace of M-matrices and Z-matrices
• Characterizations and classifications of M-matrices using generalized nullspaces
• Bounds on the indices of the spectral-circle eigenvalues of a nonnegative matrix
• On the existence of matrices with prescribed height and level characteristics
• Lower bounds for the first eigenvalue of certain M-matrices associated with graphs
• Algebraic eigenspaces of nonnegative matrices
• On the singular graph and the Weyl characteristic of an M-matrix
• The combinatorial structure of generalized eigenspaces -- from nonnegative matrices to general matrices
• Ergodic properties of nonnegative matrices. I
• Improved Upper Bounds for the Real Part of Nonmaximal Eigenvalues of Nonnegative Matrices
• Nonnegative jordan bases
• The Growth of Powers of a Nonnegative Matrix
• Combinatorial bases, derived jordan sets and the equality of the height and level characteristics of anM-matrix
• Height bases, level bases, and the equality of the height and the level characteristics of anM-matrix
• Perron components and algebraic connectivity for weighted graphs
• On nonnegative jordan chains for the generalized nullspace of a singularM-Matrix^*
• An Upper Bound for the Real Part of Nonmaximal Eigenvalues of Nonnegative Irreducible Matrices
• Convexity and Concavity of the Perron Root and Vector of Leslie Matrices with Applications to a Population Model
• On the Lidskii--Vishik--Lyusternik Perturbation Theory for Eigenvalues of Matrices with Arbitrary Jordan Structure
• A cone-theoretic approach to the spectral theory of positive linear operators: The finite-dimensional case