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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{ZVMMF_2011_51_4_a0,
     author = {Kh. D. Ikramov},
     title = {On complex matrices with simple spectrum that are unitarily similar to real matrices},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {547--554},
     year = {2011},
     volume = {51},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a0/}
}
TY  - JOUR
AU  - Kh. D. Ikramov
TI  - On complex matrices with simple spectrum that are unitarily similar to real matrices
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 547
EP  - 554
VL  - 51
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a0/
LA  - ru
ID  - ZVMMF_2011_51_4_a0
ER  - 
%0 Journal Article
%A Kh. D. Ikramov
%T On complex matrices with simple spectrum that are unitarily similar to real matrices
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 547-554
%V 51
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a0/
%G ru
%F ZVMMF_2011_51_4_a0
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/

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

[2] Pearcy C. A., “A complete set of unitary invariants for operators generating finite $W^*$-algebras of type I”, Pacific J. Math., 12 (1962), 1405–1416 | MR | Zbl

[3] Ikramov Kh. D., “O konstruktivnoi proverke vozmozhnosti oveschestvit matritsu posredstvom unitarnogo podobiya”, Zh. vychisl. matem. i matem. fiz., 50:3 (2010), 403–406 | MR | Zbl

[4] Bevis J. H., Hall F. J., Hartwig R. E., “Consimilarity and the matrix equation $A\bar X-XB=C$”, Current Trends in Matrix Theory, North-Holland, Amsterdam, 1987, 51–64 | MR