Inverse spectral problem for normal matrices and the Gauss-Lucas theorem
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- by S. M. Malamud
- Trans. Amer. Math. Soc. 357 (2005), 4043-4064
- DOI: https://doi.org/10.1090/S0002-9947-04-03649-9
- Published electronically: September 23, 2004
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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.References
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Bibliographic Information
- S. M. Malamud
- Affiliation: Departement Mathematik, HG G33.1, ETH-Zentrum, Raemistrasse 101, 8092 Zürich, Switzerland
- Email: semka@math.ethz.ch
- Received by editor(s): July 6, 2003
- Received by editor(s) in revised form: November 7, 2003
- Published electronically: September 23, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 4043-4064
- MSC (2000): Primary 15A29; Secondary 30C15, 30C10
- DOI: https://doi.org/10.1090/S0002-9947-04-03649-9
- MathSciNet review: 2159699