Changes

Möbius transformations are conformal, bilinear functions of the form

Möbius transformations are conformal, bilinear functions of the form

:<math>t = f(z) = \frac{az + b}{cz + d},</math>

<math>t = f(z) = \frac{az + b}{cz + d}</math>

where <math>t, z \in \widehat{\mathbb{C}}</math>, <math>a, b, c, d \in \mathbb{C}</math>, and <math>ad - bc \neq 0</math>.  It is an automorphism of the Riemann sphere, and the set of all Möbius transformations on the Riemann sphere forms the automorphism group.

where <math>t, z \in \widehat{\mathbb{C}}</math>, <math>a, b, c, d \in \mathbb{C}</math>, and <math>ad - bc \neq 0</math>.  It is an automorphism of the Riemann sphere, and the set of all Möbius transformations on the Riemann sphere forms the automorphism group.