Yet more elementary proofs that the determinant of a symplectic matrix is 1

DOI10.1016/j.laa.2016.11.014zbMath1352.15040OpenAlexW2556134516WikidataQ113869481 ScholiaQ113869481MaRDI QIDQ501266

Florian Bünger, Siegfried Michael Rump

Publication date: 29 December 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2016.11.014

zbMATH Keywords

isometrydeterminantsymplectic matrixtransvection

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Numerical computation of determinants (65F40) Polar geometry, symplectic spaces, orthogonal spaces (51A50) Matrices, determinants in number theory (11C20)

Related Items (2)

Equivariant Euler characteristics of symplectic buildings ⋮ Unit Triangular Factorization of the Matrix Symplectic Group

Cites Work

• The inception of symplectic geometry: The works of Lagrange and Poisson during the years 1808-1810
• Complementary bases in symplectic matrices and a proof that their determinant is one
• Two-graphs and doubly transitive groups
• The generation of \(\text{Sp}(\mathbb F_2)\) by transvections
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