Clifford algebra

Summary

Let $V$ be a vector space with a quadratic form $Q$. The Clifford algebra of $(V, Q)$ is the associative algebra generated by $V$ in which each vector $v$ squares to the scalar $Q(v)$. It contains the complex numbers, the quaternions and the exterior algebra as special cases. It is used to build spinors and spin groups, and it gives an algebraic language for rotations and reflections in geometry and physics.