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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     author = {Kh. D. Ikramov},
     title = {Criteria for {Unitary} {Congruence} of {Complex} $2\times 2$ {Matrices}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {249--260},
     publisher = {mathdoc},
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     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a7/}
}
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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/