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 -matrices satisfy Newton's inequalities |
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| Authors: | Olga Holtz |
| Institution: | Institut für Mathematik, MA 4-5, Technische Universität Berlin, D-10623 Berlin, Germany |
| Abstract: | Newton's inequalities  are shown to hold for the normalized coefficients  of the characteristic polynomial of any  - or inverse  -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. |
| Keywords: | $M$-matrices Newton's inequalities immanantal inequalities generalized matrix functions quadratic forms binomial identities nonnegative inverse eigenvalue problem |
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