We name Clifford numbers as multinomials generated by scalars (from the field of the vector space of the Clifford algebra) and the elements γ_{i} of a fixed basis for that vector space.

<1, identity matrix>

<γ_{i}, identity matrix with −1 in i^{th} diagonal position>

<γ_{i}γ_{j}, identity matrix with −1 in i^{th} and j^{th} diagonal positions>

and similarly with any product of a subset of the basis vectors.

<cos θ + (sin θ)γ_{i}γ_{j}, identity matrix
except O_{ii} = O_{jj} = cos 2θ and O_{ij} = −O_{ji} = sin 2θ>

If i, j, k and l are all distinct then

<(cos θ + (sin θ)γ_{i}γ_{j})(cos φ + (sin φ)γ_{k}γ_{l}), identity matrix
except O_{ii} = O_{jj} = cos 2θ and O_{ij} = −O_{ji} = sin 2θ, O_{kk} = O_{ll} = cos 2φ and O_{ij} = −O_{ji} = sin 2φ>