Geodesic
On a finite algorithm for calculating neutral subspaces of skew-symmetric matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 98-102 
Kh. D. Ikramov. On a finite algorithm for calculating neutral subspaces of skew-symmetric matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 98-102. http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a7/
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     author = {Kh. D. Ikramov},
     title = {On a finite algorithm for calculating neutral subspaces of skew-symmetric matrices},
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     year = {2018},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a7/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $K$ be a nonsingular skew-symmetric matrix of an even order $n = 2m$. For such a matrix, we propose a finite algorithm, using only arithmetic operations and quadratic radicals, for calculating an $m$-dimensional neutral subspace. The necessity of calculating neutral subspaces originates in the problem of solving quadratic matrix equations.

[1] Kh. D. Ikramov, “O razreshimosti odnogo klassa kvadratichnykh matrichnykh uravnenii”, Dokl. AN, 455 (2008), 135–137 | DOI

[2] C. F. Van Loan, “A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix”, Linear Algebra Appl., 16 (1984), 233–251 | DOI | MR

[3] Kh. D. Ikramov, Kh. Fassbender, “O proizvedenii dvukh kosogamiltonovykh ili dvukh kososimmetrichnykh matrits”, Zap. nauchn. semin. POMI, 359, 2008, 45–51