What is "unitary matrix"

n. (context linear algebra English) A matrix which when multiplied by its conjugate transpose yields the identity matrix.

In mathematics, a 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 Hermitian conjugate of a matrix is denoted by a dagger (†) and the equation above becomes

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.