On the construction of real canonical forms of Hamiltonian matrices whose spectrum is an imaginary pair

Abstract

If A is a Hamiltonian matrix and P a symplectic matrix, the product P −1 AP is a Hamiltonian matrix. In this paper, we consider the case where the matrix A has a pair of imaginary eigenvalues and develop an algorithm which finds a matrix P such that the matrix P −1 AP has a particularly simple form, a canonical form.