Tropical bounds for eigenvalues of matrices

Marianne Akian 1, 2 Stéphane Gaubert 1, 2 Andrea Marchesini 2, 1
1 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : We show that for all k = 1,...,n the absolute value of the product of the k largest eigenvalues of an n-by-n matrix A is bounded from above by the product of the k largest tropical eigenvalues of the matrix |A| (entrywise absolute value), up to a combinatorial constant depending only on k and on the pattern of the matrix. This generalizes an inequality by Friedland (1986), corresponding to the special case k = 1.
Type de document :
Article dans une revue
Linear Algebra and its Applications, Elsevier, 2014, 446, pp.281-303. 〈http://www.sciencedirect.com/science/article/pii/S002437951300829X〉. 〈10.1016/j.laa.2013.12.021〉
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Contributeur : Marianne Akian <>
Soumis le : jeudi 7 novembre 2013 - 17:12:10
Dernière modification le : jeudi 11 janvier 2018 - 06:22:34

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Marianne Akian, Stéphane Gaubert, Andrea Marchesini. Tropical bounds for eigenvalues of matrices. Linear Algebra and its Applications, Elsevier, 2014, 446, pp.281-303. 〈http://www.sciencedirect.com/science/article/pii/S002437951300829X〉. 〈10.1016/j.laa.2013.12.021〉. 〈hal-00881205〉

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