The action of an even Clifford element γ ∈ Cℓ 2,0 ( R ) on vectors, regarded as 1-graded elements of Cℓ 2,0 ( R ), is determined by mapping a general vector u = a 1 σ 1 + a 2 σ 2 to the vector γ γ ( u ) = γ γ u γ γ ∗ ∗ , where γ γ ∗ ∗ is the conjugate of γ γ , and the product is Clifford multiplication. In this situation, a spinor is an ordinary complex number. The action of γ γ on a spinor ϕ ϕ is given by ordinary complex multiplication: γ γ ( ϕ ϕ ) = γ γ ϕ ϕ .