On Hamiltonian Matrices, Symplectic Transformations, and Invariant Subspaces

In this paper, the reduction of a Hamiltonian matrix to a condensed form using a combination of orthogonal and non-orthogonal symplectic similarity transformations is considered. Two applications of this condensed form are described. One is concerned with the computation of the eigenvalues of the Hamiltonian matrix, and the other involves the reduction of the Hamiltonian matrix to a block upper triangular (Hamiltonian-Schur) form.