Geodesic
On sufficient conditions for the existence of a unitary congruence transformation of a given complex matrix into a real one
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIII, Tome 382 (2010), pp. 38-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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A complex $n\times n$ matrix $A$ is said to be nonderogatory if the degree of its minimal polynomial is equal to the degree of the characteristic polynomial. The aim of the paper is to prove the following proposition: Let $A\overline A$ be a nonderogatory matrix with real positive spectrum. Then $A$ can be made real by a unitary congruence transformation if and only if $A$ and $\overline A$ are unitarily congruent. Bibl. 5 titles. 
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Kh. D. Ikramov. On sufficient conditions for the existence of a unitary congruence transformation of a given complex matrix into a real one. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIII, Tome 382 (2010), pp. 38-46. http://geodesic.mathdoc.fr/item/ZNSL_2010_382_a2/

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