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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 439, Pages 99–106 (Mi znsl6203)  
How to check whether given square matrices are congruent?

Kh. D. Ikramov

Lomonosov Moscow State University, Moscow, Russia
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Abstract: Let $A$ and $B$ be square nonsingular $n$-by-$n$ matrices with entries being rational or rational Gaussian numbers. We describe a method for verifying whether these matrices are congruent. The method uses a finite number of arithmetic operations (and, in the complex case, conjugation operations).
Key words and phrases: congruences, canonical form, similarity, Jordan form, cosquare.
Received: 04.09.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 216, Issue 6, Pages 787–791
DOI: https://doi.org/10.1007/s10958-016-2943-6
Bibliographic databases:
Document Type: Article
UDC: 512.647.2
Language: Russian
Citation: Kh. D. Ikramov, “How to check whether given square matrices are congruent?”, Computational methods and algorithms. Part XXVIII, Zap. Nauchn. Sem. POMI, 439, POMI, St. Petersburg, 2015, 99–106; J. Math. Sci. (N. Y.), 216:6 (2016), 787–791
Citation in format AMSBIB
\Bibitem{Ikr15}
\by Kh.~D.~Ikramov
\paper How to check whether given square matrices are congruent?
\inbook Computational methods and algorithms. Part~XXVIII
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 439
\pages 99--106
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6203}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3502385}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 216
\issue 6
\pages 787--791
\crossref{https://doi.org/10.1007/s10958-016-2943-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84976321322}
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