Complementary bases in symplectic matrices and a proof that their determinant is one

@article{Dopico2006ComplementaryBI,
  title={Complementary bases in symplectic matrices and a proof that their determinant is one},
  author={F. Dopico and C. Johnson},
  journal={Linear Algebra and its Applications},
  year={2006},
  volume={419},
  pages={772-778}
}
New results on the patterns of linearly independent rows and columns among the blocks of a symplectic matrix are presented. These results are combined with the block structure of the inverse of a symplectic matrix, together with some properties of Schur complements, to give a new and elementary proof that the determinant of any symplectic matrix is +1. The new proof is valid for any field. Information on the zero patterns compatible with the symplectic structure is also presented. 
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