Author(s) :
Olga Holtz
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 09-2003
MSC 2000
- 15A42 Inequalities involving eigenvalues and eigenvectors
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15A15 Determinants, permanents, other special matrix functions
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15A48 Positive matrices and their generalizations; cones of matrices
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15A63 Quadratic and bilinear forms, inner products
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05E05 Symmetric functions
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05A10 Factorials, binomial coefficients, combinatorial functions
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05A17 Partitions of integers
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05A19 Combinatorial identities
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26D05 Inequalities for trigonometric functions and polynomials
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.
Keywords :
M-matrices, Newton's inequalities, immanantal inequalities, generalized matrix functions, quadratic forms, binomial identities