alternative formulation, and some authors define the operation of reflection as (minus) the sandwiching of a unit (i.e. normalized) multivector: forming rotors that are automatically normalised: The derived rotor action is then expressed as a sandwich product with the reverse: For a reflection for which the associated vector squares to a negative scalar, as may be the case with a pseudo-Euclidean space, such a vector can only be normalized up to the sign of its square, and additional bookkeeping of the sign of the application the rotor becomes necessary. The formulation in terms of the sandwich product with the inverse as above suffers no such shortcoming. Rotations of multivectors and spinors However, though as multivectors also transform double-sidedly, rotors can be combined and form a group, and so multiple rotors compose single-sidedly. The alternative formulation above is not self-normalizing and motivates the definition of spinor in geometric algebra as an object that transforms single-sidedly – i.e., spinors may be regarded as non-normalised rotors in which the reverse rather than the inverse is used in the sandwich product. Homogeneous representation algebras In homogeneous representation algebras such as conformal geometric algebra, a rotor in the representation space corresponds to a rotation about an arbitrary point, a translation or possibly another transformation in the base space. See also Double rotation Lie group Euler's formula Generator (mathematics) Versor References Geometric algebra