Geodesic
Unitary automorphisms of the space of $3\times3$ Toeplitz-plus-Hankel matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 137-151

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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 $$ \forall A\in\mathcal TH_3\longrightarrow B=U^*AU\in\mathcal TH_3. $$ 
@article{ZNSL_2014_428_a9,
     author = {Kh. D. Ikramov and A. K. Abdikalykov and V. N. Chugunov},
     title = {Unitary automorphisms of the space of $3\times3$ {Toeplitz-plus-Hankel} matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {137--151},
     publisher = {mathdoc},
     volume = {428},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a9/}
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Kh. D. Ikramov; A. K. Abdikalykov; V. N. Chugunov. Unitary automorphisms of the space of $3\times3$ Toeplitz-plus-Hankel matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 137-151. http://geodesic.mathdoc.fr/item/ZNSL_2014_428_a9/