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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 428, Pages 137–151 (Mi znsl6057)  
Unitary automorphisms of the space of $3\times3$ Toeplitz-plus-Hankel matrices

Kh. D. Ikramova, A. K. Abdikalykovb, V. N. Chugunovc

a M. V. Lomonosov Moscow State University, Moscow, Russia
b Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan
c Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia
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Abstract: Let $\mathcal TH_3$ be the set of Toeplitz-plus-Hankel $3\times3$ matrices. We describe all the matrices $U$ in the unitary group $\mathbf U_3$ such that
$$ \forall A\in\mathcal TH_3\longrightarrow B=U^*AU\in\mathcal TH_3. $$
Key words and phrases: Toeplitz matrix, Hankel matrix, Toeplitz-plus-Hankel matrix, unitary matrix, rhombus rule.
Received: 08.09.2014
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 207, Issue 5, Pages 756–766
DOI: https://doi.org/10.1007/s10958-015-2398-1
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: Kh. D. Ikramov, A. K. Abdikalykov, V. N. Chugunov, “Unitary automorphisms of the space of $3\times3$ Toeplitz-plus-Hankel matrices”, Computational methods and algorithms. Part XXVII, Zap. Nauchn. Sem. POMI, 428, POMI, St. Petersburg, 2014, 137–151; J. Math. Sci. (N. Y.), 207:5 (2015), 756–766
Citation in format AMSBIB
\Bibitem{IkrAbdChu14}
\by Kh.~D.~Ikramov, A.~K.~Abdikalykov, V.~N.~Chugunov
\paper Unitary automorphisms of the space of $3\times3$ Toeplitz-plus-Hankel matrices
\inbook Computational methods and algorithms. Part~XXVII
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 428
\pages 137--151
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6057}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 207
\issue 5
\pages 756--766
\crossref{https://doi.org/10.1007/s10958-015-2398-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84949624146}
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