%0 Journal Article %T Tropical bounds for eigenvalues of matrices %A Marianne Akian %A St¨¦phane Gaubert %A Andrea Marchesini %J Mathematics %D 2013 %I arXiv %R 10.1016/j.laa.2013.12.021 %X 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. %U http://arxiv.org/abs/1309.7319v2