Newton's inequalities cn2ββ₯cnβ1βcn+1β are shown to hold for the
normalized coefficients cnβ 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.Comment: 6 page