Möbius transformation

Möbius transformations are conformal, bilinear functions of the form

$f(z)={\frac {az+b}{cz+d}}$

where a, b, c, d are real numbers, and ad − bc ≠ 0. It is an automorphism of the Riemann Sphere, and the set of all Möbius transformations on the Riemann sphere forms the automorphism group.