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

DOI10.1016/j.laa.2006.06.014zbMath1112.15002OpenAlexW1975857703MaRDI QIDQ865438

Froilán M. Dopico, Charles R. Johnson

Publication date: 14 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2006.06.014

zbMATH Keywords

Schur complementdeterminantsymplectic matrixsymplectic transformationscomplementary basespatterns of zeros

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Hermitian, skew-Hermitian, and related matrices (15B57) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

Limit point and limit circle classification for symplectic systems on time scales ⋮ Optimal unit triangular factorization of symplectic matrices ⋮ Symplectic difference systems with periodic coefficients: Krein's traffic rules for multipliers ⋮ Each symplectic matrix is a product of four symplectic involutions ⋮ Analytical inversion of general periodic tridiagonal matrices ⋮ Unit Triangular Factorization of the Matrix Symplectic Group ⋮ Yet more elementary proofs that the determinant of a symplectic matrix is 1 ⋮ Matrices with orthogonal groups admitting only determinant one ⋮ 2n-by-2n symplectic completions of matrices of order 2n − 1 ⋮ The comparative index and transformations of linear Hamiltonian differential systems

Cites Work

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• The autonomous linear quadratic control problem. Theory and numerical solution
• Canonical forms for Hamiltonian and symplectic matrices and pencils
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• Structured tools for structured matrices
• Corrigenda to: Introduction to Symplectic Topology