Real n-dimensional projective space can be defined as (ℝ^n + 1–{0})/ℝ* (see homogeneous coordinates). So an invertible linear map T:ℝ^n + 1→ℝ^n + 1 induces a projective transformation [T]([v]) = [Tv], where [v] denotes the projective point represented by v ε‎ ℝⁿ⁺¹. The projective transformations form a group PGL(n + 1,ℝ) under composition. The group PGL(2,ℂ) is the group of Möbius transformations, acting on the Riemann sphere.