Unitary element

In mathematics, an element "x" of a *-algebra is unitary if it satisfies formula_1 
In functional analysis, a linear operator "A" from a Hilbert space into itself is called unitary if it is invertible and its inverse is equal to its own adjoint "A" and that the domain of "A" is the same as that of "A". See unitary operator for a detailed discussion. If the Hilbert space is finite-dimensional and an orthonormal basis has been chosen, then the operator "A" is unitary if and only if the matrix describing "A" with respect to this basis is a unitary matrix. 