Möbius transformation

noun1

1. •
   A transformation of the extended complex plane that is a rational function of the form f(z) = (az + b) / (cz + d), where a, b, c, d are complex numbers such that ad − bc ≠ 0; an automorphism of the complex projective line.

   • Jørgensen's inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete. — 2008