If S is a real symplectic matrix (S^T J S = J), then its spectrum is invariant under λ ↦ 1/λ; the eigenvalues therefore come in quadruples (λ, 1/λ, λ̄, 1/λ̄) off the unit circle, and in reciprocal real pairs or unit-modulus conjugate pairs…
If S is a real symplectic matrix (S^T J S = J), then its spectrum is invariant under λ ↦ 1/λ; the eigenvalues therefore come in quadruples (λ, 1/λ, λ̄, 1/λ̄) off the unit circle, and in reciprocal real pairs or unit-modulus conjugate pairs…