Question: 2.5-2. Let (Z,) be a symplectic vector space. Let A: Z Z be a linear map and assume that (IA) is invertible. Show that

2.5-2. Let (Z,) be a symplectic vector space. Let A: Z Z

2.5-2. Let (Z,) be a symplectic vector space. Let A: Z Z be a linear map and assume that (IA) is invertible. Show that A is Hamiltonian if and only if its Cayley transform (I + A)(I - A)- is symplectic. Give an example of a linear Hamiltonian vector field such that (IA) is not invertible.

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