Geodesic
Pseudo-orthogonal eigenvalues of skew-symmetric matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 92-97

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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},
     publisher = {mathdoc},
     volume = {472},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a6/}
}
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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/