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M-matrices satisfy Newton's inequalities

Holtz, Olga

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

Newton's inequalities $c_n^2\geq c_{n-1} c_{n+1}$ 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.