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.^[1] The term originated with William Kingdon Clifford,^[2] in showing that the quaternion algebra is just a special case of Hermann Grassmann's "theory of extension" (Ausdehnungslehre).^[3] Hestenes^[4] 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.