A transformation that has the form O′=UOU⁻¹, where O is an operator, U is a unitary matrix and U⁻¹ is its reciprocal, i.e. if the matrix obtained by interchanging rows and columns of U and then taking the complex conjugate of each entry, denoted U⁺, is the inverse of U; U⁺=U⁻¹. The inverse of a unitary transformation is itself a unitary transformation. Unitary transformations are important in quantum mechanics. In the Hilbert space formulation of states in quantum mechanics a unitary transformation corresponds to a rotation of axes in the Hilbert space. Such a transformation does not alter the state vector, but a given state vector has different components when the axes are rotated.