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Tropical bounds for eigenvalues of matrices

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.

preprint2013arXivOpen access
Marianne AkianStéphane GaubertAndrea Marchesini
math.COmath.SP
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Marianne AkianStéphane GaubertAndrea Marchesini

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