In linear algebra, an invertible complex square matrix U is unitary if its conjugate transpose U* is also its inverse, that is, if
where I is the identity matrix.
In physics, especially in quantum mechanics, the conjugate transpose is referred to as the Hermitian adjoint of a matrix and is denoted by a dagger (†), so the equation above is written
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.