Editing Rotation (mathematics) (section)

==Related definitions and terminology==
The ''rotation group'' is a [[Lie group]] of rotations about a [[Group action (mathematics)#Fixed points and stabilizer subgroups|fixed point]]. This (common) fixed point or [[center (geometry)|center]] is called the '''center of rotation''' and is usually identified with the [[origin (mathematics)|origin]]. The rotation group is a ''[[Group action (mathematics)#Fixed points and stabilizer subgroups|point stabilizer]]'' in a broader group of (orientation-preserving) [[motion (geometry)|motions]].

For a particular rotation:
* The ''[[axis of rotation]]'' is a [[line (geometry)|line]] of its fixed points. They exist only in {{math|''n'' {{=}} 3}}.
* The ''[[plane of rotation]]'' is a [[plane (geometry)|plane]] that is [[Group action (mathematics)#Invariant subsets|invariant]] under the rotation. Unlike the axis, its points are not fixed themselves. The axis (where present) and the plane of a rotation are [[orthogonal]].<!-- I hope not only in Euclidean and not only in 3D? --Incnis Mrsi -->

A ''representation'' of rotations is a particular formalism, either algebraic or geometric, used to parametrize a rotation map. This meaning is somehow inverse to [[group representation|the meaning in the group theory]].

Rotations of [[affine space|(affine) spaces of points]] and of respective [[vector space]]s are not always clearly distinguished. The former are sometimes referred to as ''affine rotations'' (although the term is misleading), whereas the latter are ''vector rotations''. See the article below for details.