Holtz, Olga2021-12-172021-12-172003-04-102197-8085https://depositonce.tu-berlin.de/handle/11303/15508http://dx.doi.org/10.14279/depositonce-14281Newton'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.en510 MathematikM-matricesNewton's inequalitiesimmanantal inequalitiesgeneralized matrix functionsquadratic formsbinomial identitiesResearch Paper