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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 439, Pages 93–98 (Mi znsl6202)  
Neutral subspaces of complex matrices

Kh. D. Ikramov

Lomonosov Moscow State University, Moscow, Russia
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Abstract: Consider the quadratic matrix equation $X^TDX+AX+X^TB+C=0$, where all the matrices are square and have the same order $n$. With this equation, we associate a block matrix $M$ of the double order $2n$. the solvability of the equation turns out to be related to the existence of neutral subspaces of dimension $n$ for this matrix. Reasonably general conditions ensuring the existence of such subspaces are presented.
Key words and phrases: quadratic matrix equation, neutral subspace, congruences, Jordan form, cosquare.
Received: 28.07.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 216, Issue 6, Pages 783–786
DOI: https://doi.org/10.1007/s10958-016-2942-7
Bibliographic databases:
Document Type: Article
UDC: 512.643.4
Language: Russian
Citation: Kh. D. Ikramov, “Neutral subspaces of complex matrices”, Computational methods and algorithms. Part XXVIII, Zap. Nauchn. Sem. POMI, 439, POMI, St. Petersburg, 2015, 93–98; J. Math. Sci. (N. Y.), 216:6 (2016), 783–786
Citation in format AMSBIB
\Bibitem{Ikr15}
\by Kh.~D.~Ikramov
\paper Neutral subspaces of complex matrices
\inbook Computational methods and algorithms. Part~XXVIII
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 439
\pages 93--98
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6202}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3502384}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 216
\issue 6
\pages 783--786
\crossref{https://doi.org/10.1007/s10958-016-2942-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84976260317}
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