Hamiltonian Matrix - Properties

Properties

  • Let M be a 2n × 2n block matrix given by
where A, B, C, and D are n × n matrices. Then M is a Hamiltonian matrix provided that the matrices B and C are symmetric, and that A + D* = 0.
  • The transpose of a Hamiltonian matrix is Hamiltonian.
  • The trace of a Hamiltonian matrix is zero.
  • The commutator of two Hamiltonian matrices is Hamiltonian.
  • The eigenvalues of any Hamiltonian matrix are symmetric about the imaginary axis.
  • The space of all Hamiltonian matrices is a Lie algebra .

Read more about this topic:  Hamiltonian Matrix

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