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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Inverse spectral problem for normal matrices and the Gauss-Lucas theorem


Author: S. M. Malamud
Journal: Trans. Amer. Math. Soc. 357 (2005), 4043-4064
MSC (2000): Primary 15A29; Secondary 30C15, 30C10
Published electronically: September 23, 2004
MathSciNet review: 2159699
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Abstract: We establish an analog of the Cauchy-Poincare interlacing theorem for normal matrices in terms of majorization, and we provide a solution to the corresponding inverse spectral problem. Using this solution we generalize and extend the Gauss-Lucas theorem and prove the old conjecture of de Bruijn-Springer on the location of the roots of a complex polynomial and its derivative and an analog of Rolle's theorem, conjectured by Schoenberg.


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Additional Information

S. M. Malamud
Affiliation: Departement Mathematik, HG G33.1, ETH-Zentrum, Raemistrasse 101, 8092 Zürich, Switzerland
Email: semka@math.ethz.ch

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03649-9
PII: S 0002-9947(04)03649-9
Keywords: Zeros of polynomials, normal matrices, inverse spectral problem, majorization
Received by editor(s): July 6, 2003
Received by editor(s) in revised form: November 7, 2003
Published electronically: September 23, 2004
Article copyright: © Copyright 2004 American Mathematical Society