scholarly journals Factorization of symplectic matrices into elementary factors

2020 ◽  
Vol 148 (5) ◽  
pp. 1963-1970
Author(s):  
Björn Ivarsson ◽  
Frank Kutzschebauch ◽  
Erik Løw
Keyword(s):  
Symplectic Matrices

Backward Error Analysis for Eigenproblems Involving Conjugate Symplectic Matrices

2015 ◽  
Vol 5 (4) ◽  
pp. 312-326 ◽  
Author(s):  
Wei-wei Xu ◽  
Wen Li ◽  
Xiao-qing Jin
Keyword(s):  
Optimal Control Problems ◽  
Eigenvalue Problems ◽  
Backward Error Analysis ◽  
Linear Quadratic ◽  
Backward Error ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control ◽  
Symplectic Eigenvalue ◽  
Backward Errors ◽  
Symplectic Matrices

AbstractConjugate symplectic eigenvalue problems arise in solving discrete linear-quadratic optimal control problems and discrete algebraic Riccati equations. In this article, backward errors of approximate pairs of conjugate symplectic matrices are obtained from their properties. Several numerical examples are given to illustrate the results.

Generic One Parameter Families of Symplectic Matrices

1971 ◽  
Vol 93 (1) ◽  
pp. 116 ◽  
Author(s):  
R. Clark Robinson
Keyword(s):  
Symplectic Matrices

Complex orthogonal and symplectic matrices depending on parameters

1982 ◽  
Vol 23 (5) ◽  
pp. 705-714 ◽  
Author(s):  
J. Patera ◽  
C. Rousseau
Keyword(s):  
Symplectic Matrices

scholarly journals Branching rules for unitary and symplectic matrices

2020 ◽  
Vol 48 (7) ◽  
pp. 2958-2985
Author(s):  
Uday Bhaskar Sharma ◽  
Anupam Singh
Keyword(s):  
Branching Rules ◽  
Symplectic Matrices

scholarly journals Canonical Forms for Hamiltonian and Symplectic Matrices and Pencils

1999 ◽  
Vol 302-303 ◽  
pp. 469-533 ◽  
Author(s):  
Wen-Wei Lin ◽  
Volker Mehrmann ◽  
Hongguo Xu
Keyword(s):  
Canonical Forms ◽  
Symplectic Matrices

Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group

1993 ◽  
Vol 114 (2) ◽  
pp. 235-268 ◽  
Author(s):  
Ian Melbourne ◽  
Michael Dellnitz
Keyword(s):  
Lie Group ◽  
Vector Fields ◽  
Normal Forms ◽  
Hamiltonian Vector ◽  
Compact Lie Group ◽  
The Real ◽  
Hamiltonian Vector Fields ◽  
Symplectic Action ◽  
Symplectic Matrices ◽  
Real Complex

AbstractWe obtain normal forms for infinitesimally symplectic matrices (or linear Hamiltonian vector fields) that commute with the symplectic action of a compact Lie group of symmetries. In doing so we extend Williamson's theorem on normal forms when there is no symmetry present.Using standard representation-theoretic results the symmetry can be factored out and we reduce to finding normal forms over a real division ring. There are three real division rings consisting of the real, complex and quaternionic numbers. Of these, only the real case is covered in Williamson's original work.

scholarly journals The Pfaff lattice on symplectic matrices

2010 ◽  
Vol 43 (5) ◽  
pp. 055206 ◽  
Author(s):  
Yuji Kodama ◽  
Virgil U Pierce
Keyword(s):  
Symplectic Matrices
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