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Main Title: M-matrices satisfy Newton's inequalities
Author(s): Holtz, Olga
Type: Research Paper
Abstract: 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.
Subject(s): M-matrices
Newton's inequalities
immanantal inequalities
generalized matrix functions
quadratic forms
binomial identities
Issue Date: 10-Apr-2003
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A42 Inequalities involving eigenvalues and eigenvectors
15A15 Determinants, permanents, other special matrix functions
15A48 Positive matrices and their generalizations; cones of matrices
15A63 Quadratic and bilinear forms, inner products
05E05 Symmetric functions
05A10 Factorials, binomial coefficients, combinatorial functions
05A17 Partitions of integers
05A19 Combinatorial identities
26D05 Inequalities for trigonometric functions and polynomials
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2003, 09
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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