Tropical bounds for eigenvalues of matrices
Spectral Theory
2015-04-07 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1309.7319,
title = {Tropical bounds for eigenvalues of matrices},
author = {Marianne Akian and Stéphane Gaubert and Andrea Marchesini},
journal= {arXiv preprint arXiv:1309.7319},
year = {2015}
}
Comments
17 pages, 1 figure