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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 482, Pages 120–128 (Mi znsl6829)  
Rationally verifiable necessary conditions for Hermitian congruence of complex matrices

Kh. D. Ikramov

Lomonosov Moscow State University
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Abstract: A finite computational process using arithmetic operations only is called a rational algorithm. Matrices $A$ and $F$ are said to be Hermitian congruent if $F = Q^*AQ$ for a nonsingular matrix $Q$. The paper gives a survey of necessary conditions for Hermitian congruence verifiable by rational algorithms.
Key words and phrases: $*$-congruence, rational algorithm, canonical form w.r.t. congruences, cosquare, Toeplitz decomposition.
Received: 15.01.2019
Document Type: Article
UDC: 512.643.8
Language: Russian
Citation: Kh. D. Ikramov, “Rationally verifiable necessary conditions for Hermitian congruence of complex matrices”, Computational methods and algorithms. Part XXXII, Zap. Nauchn. Sem. POMI, 482, POMI, St. Petersburg, 2019, 120–128
Citation in format AMSBIB
\Bibitem{Ikr19}
\by Kh.~D.~Ikramov
\paper Rationally verifiable necessary conditions for Hermitian congruence of complex matrices
\inbook Computational methods and algorithms. Part~XXXII
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 482
\pages 120--128
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6829}
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