Geodesic
Constructing real canonical forms of Hamiltonian matrices with two imaginary eigenvalues
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 3, pp. 687-716

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If $A$ is a Hamiltonian matrix and $P$ a symplectic matrix then 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. 
@article{FPM_1999_5_3_a3,
     author = {R. Coleman},
     title = {Constructing real canonical forms of {Hamiltonian} matrices with two imaginary eigenvalues},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {687--716},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_3_a3/}
}
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R. Coleman. Constructing real canonical forms of Hamiltonian matrices with two imaginary eigenvalues. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 3, pp. 687-716. http://geodesic.mathdoc.fr/item/FPM_1999_5_3_a3/