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

A Jacobi Algorithm in Phase Space: Diagonalizing (skew-) Hamiltonian and Symplectic Matrices with Dirac-Majorana Matrices