Geodesic
On unitarily transposable matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 39-48 
Kh. D. Ikramov. On unitarily transposable matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 39-48. http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a3/
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     author = {Kh. D. Ikramov},
     title = {On unitarily transposable matrices},
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     year = {2007},
     volume = {346},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a3/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Matrices $A\in M_n(\mathbf C)$ such that \begin{equation} A^T=Q^*AQ \tag{1} \end{equation} for a certain unitary matrix $Q$ are examined. Several classes of matrices with this property are indicated. Under certain assumptions on $A$, two conditions necessary for (1) to hold are provided.

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[6] J. Vermeer, “Examples concerning orthogonal (unitary) similarity of matrices”, Linear Algebra Appl., 428 (2008), 382–392 | DOI | MR | Zbl