Kh. D. Ikramov, A. K. Abdikalykov, V. N. Chugunov, “Unitary automorphisms of the space of <nobr>$3\times3$</nobr> Toeplitz-plus-Hankel matrices”, Zap. Nauchn. Sem. POMI, 2014, Volume 428,Pages <nobr>137

Unitary automorphisms of the space of $3\times3$ Toeplitz-plus-Hankel matrices

Kh. D. Ikramov^a, A. K. Abdikalykov^b, V. N. Chugunov^c

^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

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.

UDC: 519.6

Received: 08.09.2014