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Zapiski Nauchnykh Seminarov POMI, 2005, Volume 323, Pages 34–46 (Mi znsl378)  
This article is cited in 7 scientific papers (total in 7 papers)

On the codimension of the variety of symmetric matrices with multiple eigenvalues

M. Danaa, Kh. D. Ikramovb

a University of Kurdistan
b M. V. Lomonosov Moscow State University
Full-text PDF (185 kB) Citations (7)
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Abstract: According to a result of Wigner and von Neumann, the dimension of the set $\mathcal M$ of $n\times n$ real symmetric matrices with multiple eigenvalues is equal to $N-2$, where $N=n(n+1)/2$. This value is determined by counting the number of free parameters in the spectral decomposition of a matrix. We show that the same dimension is obtained if $\mathcal M$ is interpreted as an algebraic variety.
Received: 06.01.2005
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 137, Issue 3, Pages 4780–4786
DOI: https://doi.org/10.1007/s10958-006-0275-7
Bibliographic databases:
UDC: 512.643
Language: Russian
Citation: M. Dana, Kh. D. Ikramov, “On the codimension of the variety of symmetric matrices with multiple eigenvalues”, Computational methods and algorithms. Part XVIII, Zap. Nauchn. Sem. POMI, 323, POMI, St. Petersburg, 2005, 34–46; J. Math. Sci. (N. Y.), 137:3 (2006), 4780–4786
Citation in format AMSBIB
\Bibitem{DanIkr05}
\by M.~Dana, Kh.~D.~Ikramov
\paper On the codimension of the variety of symmetric matrices with multiple eigenvalues
\inbook Computational methods and algorithms. Part~XVIII
\serial Zap. Nauchn. Sem. POMI
\yr 2005
\vol 323
\pages 34--46
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl378}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2160306}
\zmath{https://zbmath.org/?q=an:1081.15526}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 137
\issue 3
\pages 4780--4786
\crossref{https://doi.org/10.1007/s10958-006-0275-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746797693}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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