English

Normal Forms for Symplectic Matrices

Symplectic Geometry 2014-03-20 v2

Abstract

We give a self contained and elementary description of normal forms for symplectic matrices, based on geometrical considerations. The normal forms in question are expressed in terms of elementary Jordan matrices and integers with values in {1,0,1}\{-1,0,1\} related to signatures of quadratic forms naturally associated to the symplectic matrix.

Keywords

Cite

@article{arxiv.1307.2403,
  title  = {Normal Forms for Symplectic Matrices},
  author = {Jean Gutt},
  journal= {arXiv preprint arXiv:1307.2403},
  year   = {2014}
}

Comments

27 pages updated version, propositions 12 and 17 added, uniqueness of normal form precised

R2 v1 2026-06-22T00:48:07.740Z