Canonical form for H-symplectic matrices

G. J. Groenewald*, D. B. Janse van Rensburg, A. C.M. Ran

*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceedingChapterAcademicpeer-review

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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.

Original languageEnglish
Title of host publicationOperator Theory, Analysis and the State Space Approach
Subtitle of host publicationIn Honor of Rien Kaashoek
EditorsHarm Bart, Sanne ter Horst, André C.M. Ran, Hugo J. Woerdeman
PublisherSpringer International Publishing Switzerland
Number of pages22
ISBN (Electronic)9783030042691
ISBN (Print)9783030042684
Publication statusPublished - 2018

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878


  • Canonical forms
  • H -symplectic matrices
  • Indefinite inner product space


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