Geodesic
On complex matrices with simple spectrum that are unitarily similar to real matrices
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 4, pp. 547-554 
Kh. D. Ikramov. On complex matrices with simple spectrum that are unitarily similar to real matrices. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 4, pp. 547-554. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Suppose that one should verify whether a given complex $n\times n$ matrix can be converted into a real matrix by a unitary similarity transformation. Sufficient conditions for this property to hold were found in an earlier publication of this author. These conditions are relaxed in the following way: as before, the spectrum is required to be simple, but pairs of complex conjugate eigenvalues $\lambda$, $\bar\lambda$, are now allowed. However, the eigenvectors corresponding to such eigenvalues must not be orthogonal.

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