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Canonical form for H-symplectic matrices

  • G. J. GroenewaldEmail author
  • D. B. Janse van Rensburg
  • A. C. M. Ran
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 271)

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.

Keywords

Indefinite inner product space canonical forms H -symplectic matrices 

Mathematics Subject Classification (2010).

Primary 15A21 15B57 15A63 Secondary 47B50 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • G. J. Groenewald
    • 1
  • D. B. Janse van Rensburg
    • 1
  • A. C. M. Ran
    • 2
    • 3
  1. 1.Department of MathematicsUnit for BMI, North-West UniversityPotchefstroomSouth Africa
  2. 2.Department of Mathematics, FEWVU university Amsterdam, De Boelelaan 1081aAmsterdamThe Netherlands
  3. 3.Unit for BMI, North-West UniversityPotchefstroomSouth Africa

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