Clifford algebra

A Clifford algebra is a mathematical structure that extends the real numbers to include elements that square to negative one, zero, or positive one—generalizing complex numbers and quaternions.

It provides a framework for describing rotations, reflections, and geometric transformations in spaces of any dimension.

Clifford algebras are fundamental in physics, particularly in describing spin and relativistic quantum mechanics: The Dirac equation uses a Clifford algebra to unify space and time with electron spin.