Geodesic
Matrices in Linear Mechanical Systems
Canadian mathematical bulletin, Tome 5 (1962) no. 3, pp. 253-257

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In a recent interesting paper [1] on the stability of linear mechanical systems S.P. Diliberto discusses certain reduction theorems for symmetric and skew-symmetric Hamiltonian matrices with respect to symplectic orthogonal similarity. In what follows it is shown that a unified simple argument will handle both of these problems together and then a s an example it is indicated how the argument can be also used to obtain the reduction theorem for symplectic orthogonal matrices. 
Marcus, Marvin. Matrices in Linear Mechanical Systems. Canadian mathematical bulletin, Tome 5 (1962) no. 3, pp. 253-257. doi: 10.4153/CMB-1962-025-7
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     author = {Marcus, Marvin},
     title = {Matrices in {Linear} {Mechanical} {Systems}},
     journal = {Canadian mathematical bulletin},
     pages = {253--257},
     year = {1962},
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     number = {3},
     doi = {10.4153/CMB-1962-025-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1962-025-7/}
}
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