On commuting matrices in max algebra and in classical nonnegative algebra

DOI10.1016/j.laa.2010.08.027zbMath1245.15026arXiv1005.1424OpenAlexW2963117880MaRDI QIDQ651200

Ricardo D. Katz, Hans Schneider, Sergey M. Sergeev

Publication date: 8 December 2011

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

Full work available at URL: https://arxiv.org/abs/1005.1424

zbMATH Keywords

nonnegative matricescommon eigenvectorcommuting matricesmax-plus algebramax algebraPerron-Frobenius theoryFrobenius normal formtropical algebra

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Commutativity of matrices (15A27) Positive matrices and their generalizations; cones of matrices (15B48) Max-plus and related algebras (15A80)

Related Items (14)

The tropical commuting variety ⋮ On common eigenvectors for semigroups of matrices in tropical and traditional linear algebra ⋮ Lower spectral radius and spectral mapping theorem for suprema preserving mappings ⋮ Fiedler-Pták scaling in max algebra ⋮ Dynamics of products of matrices in max algebra ⋮ The analytic hierarchy process, max algebra and multi-objective optimisation ⋮ Two cores of a nonnegative matrix ⋮ Diameters of commuting graphs of matrices over semirings ⋮ Matrices commuting with a given normal tropical matrix ⋮ On \(2 \times 2\) tropical commuting matrices ⋮ On the spectrum in max algebra ⋮ Asymptotic formulae and inequalities for point spectrum in max algebra ⋮ Applications of entropy of product systems: higher-rank graphs ⋮ Guarantees for Existence of a Best Canonical Polyadic Approximation of a Noisy Low-Rank Tensor

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• On simultaneous block-diagonalization of cyclic sequences of commuting matrices
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• Some Theorems on Commutative Matrices

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