  Jacobi's method is a well-known algorithm in linear algebra to diagonalize
symmetric matrices by successive elementary rotations. We report about the
generalization of these elementary rotations towards canonical transformations
acting in Hamiltonian phase spaces. This generalization allows to use Jacobi's
method in order to compute eigenvalues and eigenvectors of Hamiltonian (and
skew-Hamiltonian) matrices with either purely real or purely imaginary
eigenvalues by successive elementary symplectic "decoupling"-transformations.
