Unitary Matrix
(Redirected from Unitary matrix)
Jump to navigation
Jump to search
A Unitary Matrix is a complex square matrix [math]\displaystyle{ U }[/math] where [math]\displaystyle{ U^* U = UU^* = I }[/math] with I being the identity matrix and U* is the conjugate transpose of U.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/unitary_matrix Retrieved:2015-3-1.
- In mathematics, a complex square matrix U is unitary if : [math]\displaystyle{ U^* U = UU^* = I \, }[/math] where I is the identity matrix and U* is the conjugate transpose of U. In physics, especially in quantum mechanics, the Hermitian conjugate of a matrix is denoted by a dagger (†) and the equation above becomes
:: [math]\displaystyle{ U^\dagger U = UU^\dagger = I. \, }[/math] The real analogue of a unitary matrix is an orthogonal matrix. Unitary matrices have significant importance in quantum mechanics because they preserve norms, and thus, probability amplitudes.
- In mathematics, a complex square matrix U is unitary if : [math]\displaystyle{ U^* U = UU^* = I \, }[/math] where I is the identity matrix and U* is the conjugate transpose of U. In physics, especially in quantum mechanics, the Hermitian conjugate of a matrix is denoted by a dagger (†) and the equation above becomes