In quantum mechanics this means that if (π, H) or (Π, H) is a representation acting on some Hilbert space H, then the corresponding induced representation acts on the set of linear operators on H. As an example, the induced representation of the projective spin (⁠ 1 / 2 ⁠, 0) ⊕ (0, ⁠ 1 / 2 ⁠) representation on End(H) is the non-projective 4-vector (⁠ 1 / 2 ⁠, ⁠ 1 / 2 ⁠) representation.