Versal Deformations and Normal Forms for Reversible and Hamiltonian Linear Systems

The problem of this article is the characterization of equivalence classes and their versal deformations for reversible and reversible Hamiltonian matrices. In both cases the admissible transformations form a subgroup of Gl(m). Therefore the Gl(m)-orbits of a given matrix maysplitinto several -orbits. These orbits are characterized bysigns. For each sign we have a normal form and a corresponding versal deformation. The main tool in the characterization is reduction to the semi simple case.