Let TH n be the space of (T + H)-matrices of order n. The paper considers the following question: Which unitary matrices U satisfy the condition ∀A ∈ TH n → U*AU ∈ TH n ? A criterion for verifying whether a given matrix U has this property is proposed. Bibliography: 4 titles.
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Kh. D. Ikramov, “Unitary automorphisms of the space of Toeplitz matrices,” Dokl. Akad. Nauk, 456, No. 4, 389–391 (2014).
Kh. D. Ikramov, “Unitary automorphisms of the space of Hankel matrices,” Mat. Zametki, 96, No. 5, 687–696 (2014).
A. K. Abdikalykov, “Centrosymmetry of unitary matrices that preserve the set of (T+H)-matrices under similarity transformations,” Zh. Vychisl. Matem. Matem. Fiz., 55, No. 5 (2015).
Kh. D. Ikramov, V. N. Chugunov, and A. K. Abdikalykov, “On local conditions characterizing the set of (T+H)-matrices,” Dokl. Akad. Nauk, 457, No. 1, 17–18 (2014).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 428, 2014, pp. 5–12.
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Abdikalykov, A.K. Unitary Automorphisms of the Space of (T + H)-Matrices. J Math Sci 207, 669–673 (2015). https://doi.org/10.1007/s10958-015-2389-2
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DOI: https://doi.org/10.1007/s10958-015-2389-2