When dim(V) is odd, V = W ⊕ U ⊕ W ′, where U is spanned by a unit vector u orthogonal to W. The Clifford action c is defined as before on W ⊕ W ′, while the Clifford action of (multiples of) u is defined by c ( u ) α α = { α α if α α ∈ ∈ Λ Λ even W − − α α if α α ∈ ∈ Λ Λ odd W As before, one verifies that c respects the Clifford relations, and so induces a homomorphism.