Editing Rotation (mathematics) (section)

====More alternatives to the matrix formalism====
As was demonstrated above, there exist three [[multilinear algebra]] rotation formalisms: one with [[#Complex numbers|U(1), or complex numbers]], for two dimensions, and two others with [[#Quaternions|versors, or quaternions]], for three and four dimensions.

In general (even for vectors equipped with a non-Euclidean Minkowski [[quadratic form]]) the rotation of a vector space can be expressed as a [[bivector]]. This formalism is used in [[geometric algebra]] and, more generally, in the [[Clifford algebra]] representation of Lie groups.

In the case of a positive-definite Euclidean quadratic form, the double [[covering group]] of the isometry group <math>\mathrm{SO}(n)</math> is known as the [[Spin group]], <math>\mathrm{Spin}(n)</math>. It can be conveniently described in terms of a Clifford algebra. Unit quaternions give the group <math>\mathrm{Spin}(3) \cong \mathrm{SU}(2)</math>.