Abstract
Abstract Thematrices with this structure deserve special attention. From Theorem 10.1 it follows that the Hamiltonian matrices form a group (with respect to matrix sum) called sp(l, R). If we identify the vector space of real 2l ×2l matrices with R4l2, the Hamiltonian matrices form a linear subspace, of dimension l(2l + 1) (indeed, from what was previously discussed we may choose l(l + 1)/2 elements of the matrices b and c and, for example, l2 elements of the matrix a). In addition, since the Lie product (or commutator) [,] preserves the group of Hamiltonian matrices, sp(l, R) has a Lie algebra structure (see Arnol’d 1978a).
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