Rotor (mathematics)

A rotor is an object in the geometric algebra (also called Clifford algebra) of a vector space that represents a rotation about the origin. More precisely, for each rotation there exist two rotors that represent it. The term originated with William Kingdon Clifford, in showing that the quaternion algebra is just a special case of Hermann Grassmann's "theory of extension" (Ausdehnungslehre). Hestenes defined a rotor to be any element ${\displaystyle R}$ of a geometric algebra that can be written as the product of an even number of unit vectors and satisfies ${\displaystyle R{\tilde {R}}=1}$, where ${\displaystyle {\tilde {R}}}$ is the "reverse" of ${\displaystyle R}$—that is, the product of the same vectors, but in reverse order.