Geodesic
Criteria for Unitary Congruence of Complex $2\times 2$ Matrices
Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 249-260.

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Canonical forms of $2\times 2$ matrices with respect to unitary congruence transformations are described. This makes it possible to formulate simple criteria for checking whether the given matrices are unitarily congruent.
Keywords: unitary similarity transformation, unitary congruence transformation, Specht's criterion, singular value, cosquare, Jordan block. 
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Kh. D. Ikramov. Criteria for Unitary Congruence of Complex $2\times 2$ Matrices. Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 249-260. http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a7/

[1] R. Khorn, Ch. Dzhonson, Matrichnyi analiz, Mir, M., 1989 | MR | Zbl

[2] C. Pearcy, “A complete set of unitary invariants for operators generating finite $W^*$-algebras of type I”, Pacific J. Math., 12 (1962), 1405–1416 | MR | Zbl

[3] Y. Hong, R. A. Horn, “A characterization of unitary congruence”, Linear and Multilinear Algebra, 25:2 (1989), 105–119 | DOI | MR | Zbl

[4] Kh. D. Ikramov, “O matrichnom uravnenii $X\overline X=A$”, Dokl. RAN, 424:3 (2009), 304–307 | MR