On the product of two skew-Hamiltonian or two skew-symmetric matrices |
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Authors: | Kh D Ikramov H Fassbender |
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Institution: | 1.Moscow State University,Moscow,Russia;2.Technische Universit?t Braunschweig,Braunschweig,Germany |
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Abstract: | 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 corresponding to 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 reduces to the computation of the eigenvalues of a similar skew-Hamiltonian matrix.
Bibliography: 8 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 359, 2008, pp. 45–51. |
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