Versor

In modern algebra, a versor or unit quaternion is a quaternion of norm one. Every versor is of the form

Such a versor may be viewed as a directed great-circle arc with axis r and length a. In case a = π/2, the versor is a right versor. In linear algebra, geometry, and physics, the term versor is often used for a right versor. In this case, a versor is defined as a unit vector indicating the orientation of a directed axis in a Cartesian coordinate system.

When used to represent a rotation, a versor will rotate any quaternion vector v through the angle θ around the unit vector r through the sandwiching product qvq−1.

The word is from Latin versus = "turned", from pp. of vertere = "to turn", and was introduced by William Rowan Hamilton, in the context of his quaternion theory.