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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 3, Pages 85–88
DOI: https://doi.org/10.4213/faa162 (Mi faa162) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Brief communications

An Analog of the Poincaré Separation Theorem for Normal Matrices and the Gauss–Lucas Theorem

S. M. Malamud

Swiss Federal Institute of Technology
Full-text PDF (121 kB) Citations (10)
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DOI: https://doi.org/10.4213/faa162
Abstract: We establish an analog of the Cauchy–Poincaré separation theorem for normal matrices in terms of majorization. A solution to the inverse spectral problem (Borg type result) is also presented. Using this result, we generalize and extend the Gauss–Lucas theorem about the location of roots of a complex polynomial and of its derivative. The generalization is applied to prove old conjectures due to de Bruijn–Springer and Schoenberg.
Keywords: normal matrix, majorization, zeros of polynomials, Gauss–Lucas theorem, Cauchy–Poincaré separation theorem, inverse problem.
Received: 01.10.2002
English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 3, Pages 232–235
DOI: https://doi.org/10.1023/A:1026044902927
Bibliographic databases:
Document Type: Article
UDC: 517+512.64
Language: Russian
Citation: S. M. Malamud, “An Analog of the Poincaré Separation Theorem for Normal Matrices and the Gauss–Lucas Theorem”, Funktsional. Anal. i Prilozhen., 37:3 (2003), 85–88; Funct. Anal. Appl., 37:3 (2003), 232–235
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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