matrices satisfy Newton's inequalities
Author:
Olga Holtz
Journal:
Proc. Amer. Math. Soc. 133 (2005), 711717
MSC (2000):
Primary 15A42; Secondary 15A15, 15A45, 15A48, 15A63, 05E05, 05A10, 05A17, 05A19, 26D05, 65F18
Published electronically:
August 24, 2004
MathSciNet review:
2113919
Fulltext PDF Free Access
Abstract 
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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 45, Technische Universität Berlin, D10623 Berlin, Germany
Address at time of publication:
Department of Mathematics, University of CaliforniaBerkeley, 821 Evans Hall, Berkeley, California 94720
Email:
holtz@math.TUBerlin.DE, holtz@math.berkeley.edu
DOI:
http://dx.doi.org/10.1090/S0002993904075768
PII:
S 00029939(04)075768
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
