-matrices satisfy Newton's inequalities

Author:
Olga Holtz

Journal:
Proc. Amer. Math. Soc. **133** (2005), 711-717

MSC (2000):
Primary 15A42; Secondary 15A15, 15A45, 15A48, 15A63, 05E05, 05A10, 05A17, 05A19, 26D05, 65F18

Published electronically:
August 24, 2004

MathSciNet review:
2113919

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Olga Holtz**

Affiliation:
Institut für Mathematik, MA 4-5, Technische Universität Berlin, D-10623 Berlin, Germany

Address at time of publication:
Department of Mathematics, University of California-Berkeley, 821 Evans Hall, Berkeley, California 94720

Email:
holtz@math.TU-Berlin.DE, holtz@math.berkeley.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07576-8

Keywords:
$M$-matrices,
Newton's inequalities,
immanantal inequalities,
generalized matrix functions,
quadratic forms,
binomial identities,
nonnegative inverse eigenvalue problem.

Received by editor(s):
March 20, 2003

Received by editor(s) in revised form:
November 21, 2003

Published electronically:
August 24, 2004

Additional Notes:
The author is on leave from the Department of Computer Science, University of Wisconsin, Madison, WI 53706, and is supported by the Alexander von Humboldt Foundation.

Communicated by:
Lance W. Small

Article copyright:
© Copyright 2004
American Mathematical Society