Normal operators are a class of linear operators in functional analysis that commute with their adjoint. This means that if A is a normal operator, then A A^* = A^* A , where A^* is the adjoint of A . Normal operators include important examples such as self-adjoint operators, unitary operators, and normal matrices. These operators have several useful properties, including the ability to be diagonalized by a complete set of orthonormal eigenvectors. This makes them particularly significant in quantum mechanics and other areas of physics, where they often represent observable quantities.