Some simple examples of spinors in low dimensions arise from considering the even-graded subalgebras of the Clifford algebra Cℓ p, q ( R ). This is an algebra built up from an orthonormal basis of n = p + q mutually orthogonal vectors under addition and multiplication, p of which have norm +1 and q of which have norm −1, with the product rule for the basis vectors e i e j = { + 1 i = j , i ∈ ∈ ( 1 , … … , p ) − − 1 i = j , i ∈ ∈ ( p + 1 , … … , n ) − − e j e i i ≠ ≠ j .