On the Collatz-Wielandt sets associated with a cone-preserving map

DOI10.1016/0024-3795(89)90033-5zbMath0684.15008OpenAlexW2061409307MaRDI QIDQ1825253

Shiow-Fang Wu, Bit-Shun Tam

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0024-3795(89)90033-5

zbMATH Keywords

conespectral radiusnonnegative matrixlinear inequalitiescone-preserving mapPerron-Frobenius theoremCollatz-Wielandt numbersnonnegativity of solutionsCollatz-Wielandt sets

Mathematics Subject Classification ID

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

Related Items (11)

Optimal networked state estimation in the presence of multi-channel correlated packet losses ⋮ Existence of a Mean-Square Stabilizing Solution to a Modified Algebraic Riccati Equation ⋮ On the penetration distance in Garside monoids ⋮ On the distinguished eigenvalues of a cone-preserving map ⋮ Characterizations of spectral radius of positive operators of \(C^*\) algebras ⋮ Collatz-Wielandt numbers in general partially ordered spaces ⋮ The Perron generalized eigenspace and the spectral cone of a cone-preserving map ⋮ On the Core of a Cone-Preserving Map ⋮ Maximal exponents of polyhedral cones (III) ⋮ On the invariant faces associated with a cone-preserving map ⋮ Linear equations over cones and Collatz-Wielandt numbers

Cites Work

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• On the Collatz-Wielandt numbers and the local spectral radius of a nonnegative operator
• On the distinguished eigenvalues of a cone-preserving map
• The influence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: a survey
• Theory of cones
• Geometric conditions for the existence of positive eigenvalues of matrices
• Characterizations of spectral radius of positive operators of \(C^*\) algebras
• Algebraic Perron-Frobenius theory
• Algebraic eigenspaces of nonnegative matrices
• Nested bounds for the spectral radius
• Unzerlegbare, nicht negative Matrizen
• On Nonnegative Solutions of Matrix Equations
• The Growth of Powers of a Nonnegative Matrix

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