Canonical form for H-symplectic matrices
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Groenewald, G.J.
Janse van Rensburg, D.B.
Ran, A.C.M.
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Springer
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Abstract
In this paper we consider pairs of matrices (A,H), with A and H either both real or both complex, H is invertible and skew-symmetric and A is H -symplectic, that is, ATH A = H. A canonical form for such pairs is derived under the transformations (A,H) → (S −1AS, STH S) for invertible matrices S. In the canonical form for the pair, the matrix A is brought in standard (real or complex) Jordan normal form, in contrast to existing canonical forms
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Groenewald, G.J. et al. 2018. Canonical form for H-symplectic matrices. (In Bart, H., Ter Horst, S., Ran, A.C.M. & Woerdeman, H.J., eds. Operator theory, analysis and the state space approach: in Honor of Rien Kaashoek). Operator theory: advances and applications, 271:269-290. [https://doi.org/10.1007/978-3-030-04269-1_11]