# Unitary Matrix

A Unitary Matrix is a complex square matrix [math]U[/math] where [math] 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] 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] 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