111 citations · 694 across the 56 of their papers we have counts for
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math.SP2013★ 16 cited
Tropical bounds for eigenvalues of matrices
Marianne Akian, Stéphane Gaubert, Andrea Marchesini
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…
math.SP2013★ 15 cited
Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots
Marianne Akian, Stephane Gaubert, Meisam Sharify
We show that the sequence of moduli of the eigenvalues of a matrix polynomial is log-majorized, up to universal constants, by a sequence of "tropical roots" depending only on the n…