M-matrices satisfy Newton's inequalities

Details M-matrices satisfy Newton's inequalities M-matrices satisfy Newton's inequalities

2005-12-27

arxiv.org/abs/math/0512610v1

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

Mathematics

Rings and Algebras

6 pages

Scientific paper

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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