This article is cited in 3 papers

Centrosymmetric property of unitary matrices that preserve the set of $(T+H)$-matrices under similarity transformations

A. K. Abdikalykov

Kazakhstan Division of the Moscow State University, ul. Munaitpasova 7, Astana, 010010, Kazakhstan

Abstract: The following problem is discussed: what are unitary $n\times n$ matrices $U$ that map the linear space of $(T+H)$-matrices into itself by similarity transformations? Analogous problems for the spaces of Toeplitz and Hankel matrices were solved recently. For $(T+H)$-matrices, the problem of describing appropriate matrices $U$ appears to be considerably more complex and is still open. The result proved in this paper may contribute to the complete solution of this problem. Namely, every such matrix $U$ is either centrosymmetric or skew-centrosymmetric; moreover, only the first variant is possible for odd $n$.

Key words: unitary similarity, $(T+H)$-matrix, centrosymmetric matrix.

UDC: 519.61

MSC: 15B10

Received: 23.09.2014

DOI: 10.7868/S0044466915050026

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:5, 731–733

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