Hamiltonian Matrix

1 Hamiltonian Matrix

The Hamiltonian matrix is a \(2n\times 2n\) matrix \(A\) such that \(JA\) is symmetric, where \(J\) is the skew-symmetric matrix \[ J=\begin{bmatrix} 0_{n} & I_{n} \\ -I_{n} & 0_{n} \end{bmatrix} \] and \(I_{n}\) is the \(n \times n\) identity matrix.