Geodesic
Unitary automorphisms of the space of $(T+H)$-matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 5-12

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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 $\forall A\in TH_n\to U^*AU\in TH_n$? A criterion for verifying whether a given matrix $U$ has this property is proposed. 
@article{ZNSL_2014_428_a0,
     author = {A. K. Abdikalykov},
     title = {Unitary automorphisms of the space of $(T+H)$-matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--12},
     publisher = {mathdoc},
     volume = {428},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a0/}
}
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A. K. Abdikalykov. Unitary automorphisms of the space of $(T+H)$-matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 5-12. http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a0/