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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 482, Pages 129–134 (Mi znsl6830)  

Congruence criteria for normal and conjugate-normal matrices

Kh. D. Ikramov

Lomonosov Moscow State University
References:
Abstract: Complex $n\times n$ matrices $A$ and $B$ are said to be $T$-congruent if $B = S^T AS$ and $*$-congruent if $B = S^* AS$, where $S$ is an arbitrary nonsingular matrix. For several facts related to normal matrices and $*$-congruences, analogs in the theory of $T$-congruences, concerning conjugate-normal matrices, are found.
Key words and phrases: $*$-congruence, $T$-congruence, similarity, consimilarity, unitary congruence, polar decomposition.
Received: 18.01.2019
Document Type: Article
UDC: 512.643.8
Language: Russian
Citation: Kh. D. Ikramov, “Congruence criteria for normal and conjugate-normal matrices”, Computational methods and algorithms. Part XXXII, Zap. Nauchn. Sem. POMI, 482, POMI, St. Petersburg, 2019, 129–134
Citation in format AMSBIB
\Bibitem{Ikr19}
\by Kh.~D.~Ikramov
\paper Congruence criteria for normal and conjugate-normal matrices
\inbook Computational methods and algorithms. Part~XXXII
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 482
\pages 129--134
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6830}
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  • https://www.mathnet.ru/eng/znsl/v482/p129
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