Geodesic
Simultaneous decomplexification of a pair of complex matrices via a unitary similarity transformation
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 5-8 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $(A,B)$ be a given pair of complex $n\times n$ matrices and let at least one of these matrices be unitarily irreducible. An algorithm for verifying whether $A$ and $B$ can be made real via the same unitary similarity transformation is proposed and justified. 
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A. K. Abdikalykov; Kh. D. Ikramov. Simultaneous decomplexification of a pair of complex matrices via a unitary similarity transformation. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 5-8. http://geodesic.mathdoc.fr/item/ZNSL_2011_395_a0/

[1] Kh. D. Ikramov, “O kompleksnykh matritsakh, unitarno podobnykh veschestvennym matritsam”, Mat. zametki, 88:6 (2010), 840–847 | DOI | MR

[2] Kh. D. Ikramov, “O latentno-veschestvennykh matritsakh i blochnykh kvaternionakh”, Zap. nauchn. semin. POMI, 382, 2010, 47–54 | MR

[3] Kh. D. Ikramov, “O konechnykh algoritmakh dlya proverki unitarnogo podobiya i unitarnoi kongruentnosti pary kompleksnykh matrits”, Dokl. RAN, 437:2 (2011), 151–153 | MR | Zbl

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

[5] Kh. D. Ikramov, “Ob odnom kriterii kvazidiagonalizuemosti veschestvennykh matrits”, Zh. vychisl. matem. i matem. fiz., 40:1 (2000), 6–20 | MR | Zbl