On the factorisation of matrix elements for systems with anti-unitary symmetry

For the case of corepresentations of anti-unitary magnetic groups a new generalisation of the Wigner-Eckart theorem, based on the symmetrised Clebsch-Gordan coefficients, or 3D-symbols, is given. It is shown that the reduced matrix elements are real for all types of corepresentations. The reduced matrix elements of coupled tensor operators are expressed in terms of the reduced matrix elements of their components.