We now consider systems with two physically different angular momenta j 1 and j 2. Examples include the spin and the orbital angular momentum of a single electron, or the spins of two electrons, or the orbital angular momenta of two electrons. Mathematically, this means that the angular momentum operators act on a space V 1 of dimension 2 j 1 + 1 and also on a space V 2 of dimension 2 j 2 + 1 . We are then going to define a family of "total angular momentum" operators acting on the tensor product space V 1 ⊗ ⊗ V 2 , which has dimension ( 2 j 1 + 1 ) ( 2 j 2 + 1 ) . The action of the total angular momentum operator on this space constitutes a representation of the SU(2) Lie algebra, but a reducible one. The reduction of this reducible representation into irreducible pieces is the goal of Clebsch–Gordan theory.