Geodesic
On Unitary Transposable Matrices of Order Three
Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 563-570

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A matrix $A \in M_n(\mathbb{C})$ is said to be unitarily transposable if $$ A^T=Q^*AQ $$ for a certain unitary matrix $Q$. Every $2\times 2$ matrix is unitarily transposable; however, for greater orders, a similar statement is false, and the general description of unitarily transposable matrices of order $n$ is at present unknown. We give such a description for matrices of order three.
Keywords: unitary transposable matrix, unitary similarity, Specht's criterion, Schur form, persymmetric matrix, geometric multiplicity. 
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     author = {Kh. D. Ikramov and A. K. Abdikalykov},
     title = {On {Unitary} {Transposable} {Matrices} of {Order} {Three}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a8/}
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Kh. D. Ikramov; A. K. Abdikalykov. On Unitary Transposable Matrices of Order Three. Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 563-570. http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a8/