Geodesic
On the product of two skew-Hamiltonian matrices or two skew-symmetric matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 45-51

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We show that the product $C$ of two skew-Hamiltonian matrices obeys the Stenzel conditions. If at least one of the factors is nonsingular, then the Stenzel conditions amount to the requirement that every elementary divisor for a nonzero eigenvalue of $C$ occurs an even number of times. The same properties are valid for the product of two skew-pseudosymmetric matrices. We observe that the method proposed by Van Loan for computing the eigenvalues of real Hamiltonian and skew-Hamiltonian matrices can be extended to complex skew-Hamiltonian matrices. Finally, we show that the computation of the eigenvalues of a product of two skew-symmetric matrices can be reduced to computing the eigenvalues of a similar skew-Hamiltonian matrix. Bibl. – 8 titles. 
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     author = {Kh. D. Ikramov and H. Fassbender},
     title = {On the product of two {skew-Hamiltonian} matrices or two skew-symmetric matrices},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a5/}
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Kh. D. Ikramov; H. Fassbender. On the product of two skew-Hamiltonian matrices or two skew-symmetric matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 45-51. http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a5/