Editing Rotation matrix (section)

=== Vector to vector formulation ===
In some instances it is interesting to describe a rotation by specifying how a vector is mapped into another through the shortest path (smallest angle). In <math>\mathbb{R}^3</math> this completely describes the associated rotation matrix. In general, given {{math|''x'', ''y'' ∈ <math>\mathbb{S}</math><sup>''n''</sup>}}, the matrix
:<math>R:=I+y x^\mathsf{T}-x y^\mathsf{T}+\frac{1}{1+\langle x,y\rangle}\left(yx^\mathsf{T}-xy^\mathsf{T}\right)^2</math>
belongs to {{math|SO(''n'' + 1)}} and maps {{mvar|x}} to {{mvar|y}}.<ref>{{cite journal |last1=Cid |first1=Jose Ángel |last2=Tojo |first2=F. Adrián F. |title=A Lipschitz condition along a transversal foliation implies local uniqueness for ODEs |journal=Electronic Journal of Qualitative Theory of Differential Equations |year=2018 |volume=13 |issue=13 |pages=1–14 |doi=10.14232/ejqtde.2018.1.13 |arxiv=1801.01724 |url=http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=6497|doi-access=free }}</ref>