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
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)