𝑀-matrices satisfy Newton’s inequalities

Holtz, Olga

doi:10.1090/S0002-9939-04-07576-8

$M$-matrices satisfy Newton’s inequalities
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by Olga Holtz

Proc. Amer. Math. Soc. 133 (2005), 711-717

DOI: https://doi.org/10.1090/S0002-9939-04-07576-8

Published electronically: August 24, 2004

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Abstract:

Newton’s inequalities $c_n^2 \ge c_{n-1}c_{n+1}$ are shown to hold for the normalized coefficients $c_n$ of the characteristic polynomial of any $M$- or inverse $M$-matrix. They are derived by establishing first an auxiliary set of inequalities also valid for both of these classes. They are also used to derive some new necessary conditions on the eigenvalues of nonnegative matrices.

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