Quaternions and Clifford Algebras

Quaternions are a type of hypercomplex numbers. Unit quaternions, which describe rotations, were called versors by Hamilton. The concept of versor can be generalized as the product of invertible vectors in the Clifford algebra. Clifford algebras are also named geometric algebras, when referring to the subset of nondegenerate Clifford algebras. Quaternions are four-dimensional elements that form an algebra. Unit quaternions are used to express three-dimensional rotations in a compact way, and their algebraic structure allows performing all related operations, such as composition of rotations, inverse rotations, and action of a rotation on a geometric objectPeer ReviewedPostprint (published version