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Tropical bounds for the eigenvalues of block structured matrices

Marianne Akian 1, 2 Stephane Gaubert 1, 2 Andrea Marchesini 2, 1
2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We establish a log-majorization inequality, which relates the moduli of the eigenvalues of a block structured matrix with the tropical eigenvalues of the matrix obtained by replacing every block entry of the original matrix by its norm. This inequality involves combinatorial constants depending on the size and pattern of the matrix. Its proof relies on diagonal scalings, constructed from the optimal dual variables of a parametric optimal assignment problem.
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Contributor : Marianne Akian <>
Submitted on : Thursday, January 7, 2016 - 3:01:31 PM
Last modification on : Friday, April 30, 2021 - 9:56:03 AM


  • HAL Id : hal-01252379, version 1


Marianne Akian, Stephane Gaubert, Andrea Marchesini. Tropical bounds for the eigenvalues of block structured matrices. SIAM Conference on Applied Linear Algebra (SIAM LA), Oct 2015, Atlanta, United States. ⟨hal-01252379⟩



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