Let V be an n-dimensional linear space over a field K, and let Q be a quadratic form on V. A Clifford algebra is then defined over T(V)/I(Q), where T(V) is the tensor algebra over V and I is a particular ideal of T(V). Clifford algebraists call their higher dimensional numbers hypercomplex even though they do not share all the properties of complex numbers and no classical function theory can be constructed over them.

algebra | hypercomplex number | quaternion | spinor | spinor field | vector space