Geodesic
Centrosymmetric property of unitary matrices that preserve the set of $(T+H)$-matrices under similarity transformations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5, pp. 739-741 
A. K. Abdikalykov. Centrosymmetric property of unitary matrices that preserve the set of $(T+H)$-matrices under similarity transformations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5, pp. 739-741. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a0/
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     title = {Centrosymmetric property of unitary matrices that preserve the set of $(T+H)$-matrices under similarity transformations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $n$.

[1] Ikramov Kh. D., Chugunov V. N., Abdikalykov A. K., “O lokalnykh usloviyakh, kharakterizuyuschikh prostranstvo $(T+H)$-matrits”, Dokl. AN, 457:1 (2014), 17–18 | Zbl

[2] Ikramov Kh. D., “Unitarnye avtomorfizmy prostranstva teplitsevykh matrits”, Dokl. AN, 456:4 (2014), 389–391 | Zbl

[3] Ikramov Kh. D., “Unitarnye avtomorfizmy prostranstva gankelevykh matrits”, Matem. zametki, 96:5 (2014), 687–696 | Zbl