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.
Dedicated to Rien Kaashoek on the occasion of his eightieth birthday
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Groenewald, G.J., Janse van Rensburg, D.B., Ran, A.C.M. (2018). Canonical form for H-symplectic matrices. In: Bart, H., ter Horst, S., Ran, A., Woerdeman, H. (eds) Operator Theory, Analysis and the State Space Approach. Operator Theory: Advances and Applications, vol 271. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04269-1_11
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DOI: https://doi.org/10.1007/978-3-030-04269-1_11
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-04268-4
Online ISBN: 978-3-030-04269-1
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