holds, where A and B are defined as in the first section. This can hold only if A i and B i have the same dimensions, i.e. only if m = n. When m ≠ n then (m, n) ⊕ (n, m) can be extended to an irreducible representation of SO(3; 1), the orthochronous Lorentz group. The parity reversal representative Π(P) does not come automatically with the general construction of the (m, n) representations. It must be specified separately. The matrix β = i γ (or a multiple of modulus −1 times it) may be used in the (⁠ 1 / 2 ⁠, 0) ⊕ (0, ⁠ 1 / 2 ⁠) representation.