Canonical Forms for Hamiltonian and Symplectic Matrices and Pencils Original Research Article

We study canonical forms for Hamiltonian and symplectic matrices or pencils under equivalence transformations which keep the class invariant. In contrast to other canonical forms our forms are as close as possible to a triangular structure in the same class. We give necessary and sufficient conditions for the existence of Hamiltonian and symplectic triangular Jordan, Kronecker and Schur forms. The presented results generalize results of Lin and Ho W.-W. Lin, T.-C. Ho, On Schur type decompositions for Hamiltonian and symplectic pencils, Technical report, Institute of Applied Mathematics, National Tsing Hua University, Taiwan, 1990 and simplify the proofs presented there.