Geodesic
On a constructive procedure for verifying whether a matrix can be made real by a unitary similarity transformation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 403-406

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There are well-known conditions under which a complex $n\times n$ matrix $A$ can be made real by a similarity transformation. Under the additional assumption that $A$ has a simple real spectrum, a constructive answer is given to the question whether this transformation can be realized via a unitary rather than arbitrary similarity. 
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     title = {On a constructive procedure for verifying whether a matrix can be made real by a unitary similarity transformation},
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Kh. D. Ikramov. On a constructive procedure for verifying whether a matrix can be made real by a unitary similarity transformation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 403-406. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a0/