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New symplectic transformations: Symplectic reflector on C2n_2

S. Agoujil, A.H. Bentbib


The aim of this paper is to describe new symplectic complex transformations based on symplectic reflectors in C2n_2. Our idea is to work on C2n_2 as free module on the ring K=C2n_2 instead of a vector space structure on C2n. This transformations are defined in parallel with the classical elementary reflectors. Interesting properties allow us to construct new algorithms for computing an SR factorization. Some numerical experiments are given.


SR decompositions -Indefinite symplectic inner product - Symplectic reflector -Symplectic Householder

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