Geodesic
Pseudo-orthogonal eigenvalues of skew-symmetric matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 92-97 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The following result is attributed to J. Williamson: Every real, symmetric, and positive definite matrix $A$ of even order $n = 2m$ can be brought to diagonal form by congruence with a symplectic transformation matrix. The diagonal entries of this form are invariants of congruence transformations performed with $A$ and are called the symplectic eigenvalues of this matrix. In this short paper, we prove an analogous fact concerning (complex) skew-symmetric matrices and transformations belonging to a different group, namely, the group of pseudo-orthogonal matrices. 
@article{ZNSL_2018_472_a6,
     author = {Kh. D. Ikramov},
     title = {Pseudo-orthogonal eigenvalues of skew-symmetric matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {92--97},
     year = {2018},
     volume = {472},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a6/}
}
TY  - JOUR
AU  - Kh. D. Ikramov
TI  - Pseudo-orthogonal eigenvalues of skew-symmetric matrices
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 92
EP  - 97
VL  - 472
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a6/
LA  - ru
ID  - ZNSL_2018_472_a6
ER  - 
%0 Journal Article
%A Kh. D. Ikramov
%T Pseudo-orthogonal eigenvalues of skew-symmetric matrices
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 92-97
%V 472
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a6/
%G ru
%F ZNSL_2018_472_a6
Kh. D. Ikramov. Pseudo-orthogonal eigenvalues of skew-symmetric matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 92-97. http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a6/

[1] J. Williamson, “On the algebraic problem concerning the normal form of linear dynamical systems”, Amer. J. Math., 58 (1936), 141–163 | DOI | MR

[2] Kh. D. Ikramov, “O simplekticheskikh sobstvennykh znacheniyakh polozhitelno opredelennykh matrits”, Vestnik Mosk. un-ta. Ser. 15. Vychisl. mat. kibernetika, 2018, no. 1, 3–6

[3] A. I. Maltsev, Osnovy lineinoi algebry, Nauka, M., 1970

[4] Kh. D. Ikramov, “O singulyarnykh chislakh i polyarnom razlozhenii operatora v bilineino metricheskom prostranstve”, ZhVM i MF, 28 (1988), 127–129