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- W2006979232 abstract "Let λ1,…,λn denote the eigenvalues of a n×n matrix, ordered by nonincreasing absolute value, and let γ1≥⋯≥γn denote the tropical eigenvalues of an associated n×n matrix, obtained by replacing every entry of the original matrix by its absolute value. We show that for all 1≤k≤n, |λ1⋯λk|≤Cn,kγ1⋯γk, where Cn,k is 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." @default.
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- W2006979232 date "2014-04-01" @default.
- W2006979232 modified "2023-10-18" @default.
- W2006979232 title "Tropical bounds for eigenvalues of matrices" @default.
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- W2006979232 doi "https://doi.org/10.1016/j.laa.2013.12.021" @default.
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