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Journal Articles Linear Algebra and its Applications Year : 2014

Tropical bounds for eigenvalues of matrices

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.

Dates and versions

hal-00881205 , version 1 (07-11-2013)

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Cite

Marianne Akian, Stéphane Gaubert, Andrea Marchesini. Tropical bounds for eigenvalues of matrices. Linear Algebra and its Applications, 2014, 446, pp.281-303. ⟨10.1016/j.laa.2013.12.021⟩. ⟨hal-00881205⟩
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