A rotor is an n-blade object in geometric algebra

Geometric algebra

Geometric algebra , together with the associated Geometric calculus, provides a comprehensive alternative approach to the algebraic representation of classical, computational and relativistic geometry. GA now finds application in all of physics, in graphics and in robotics...

, which rotates another n-blade object about a fixed or translated

Translation (geometry)

In Euclidean geometry, a translation moves every point a constant distance in a specified direction. A translation can be described as a rigid motion, other rigid motions include rotations and reflections. A translation can also be interpreted as the addition of a constant vector to every point, or...

 point

Point (geometry)

In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...

. They are normally motivated by considering an even number of reflections, which generate rotations (see also the Cartan–Dieudonné theorem). Reflections in geometric algebra are handled via (minus) sandwiching multivectors between a unit vector perpendicular to the hyperplane of reflection. Thus rotors are automatically normalised . Under a rotation generated by the rotor , a general multivector

Multivector

In multilinear algebra, a multivector or clif is an element of the exterior algebra on a vector space, \Lambda^* V. This algebra consists of linear combinations of simple k-vectors v_1\wedge\cdots\wedge v_k."Multivector" may mean either homogeneous elements In multilinear algebra, a multivector...

  will transform double-sidedly as
. However, as rotors can be combined and follow a group

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...

 multiplication law, rotors themselves transform single-sidedly under further rotations. This in particular motivates the definition of spinor

Spinor

In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...

in geometric algebra as an object that transforms single-sidedly — i.e. spinors are essentially unnormalised rotors.