Editing Projective linear group (section)

== Elements ==
The elements of the projective linear group can be understood as "tilting the plane" along one of the axes, and then projecting to the original plane, and also have dimension ''n''.

[[File:Riemann sphere1.svg|thumb|Rotation about the ''z'' axes rotates the projective plane, while the projectivization of rotation about lines parallel to the ''x'' or ''y'' axes yield projective rotations of the plane.]]
A more familiar geometric way to understand the projective transforms is via '''projective rotations''' (the elements of {{nowrap|PSO(''n'' + 1)}}), which corresponds to the [[stereographic projection]] of rotations of the unit hypersphere, and has dimension {{tmath|1= \textstyle{1+2+\cdots+n=\binom{n+1}{2} } }}. Visually, this corresponds to standing at the origin (or placing a camera at the origin), and turning one's angle of view, then projecting onto a flat plane. Rotations in axes perpendicular to the [[hyperplane]] preserve the hyperplane and yield a rotation of the hyperplane (an element of SO(''n''), which has dimension {{tmath|1= \textstyle{1+2+\cdots+(n-1) =\binom{n}{2} } }}.), while rotations in axes parallel to the hyperplane are proper projective maps, and accounts for the remaining ''n'' dimensions.