About: Normal element

In mathematics, an element x of a *-algebra is normal if it satisfies This definition stems from the definition of a normal linear operator in functional analysis, where a linear operator A from a Hilbert space into itself is called unitary if where the adjoint of A is A∗ and the domain of A is the same as that of A∗. See normal operator for a detailed discussion. If the Hilbert space is finite-dimensional and an orthonormal basis has been chosen, then the operator A is normal if and only if the matrix describing A with respect to this basis is a normal matrix.