Difference between revisions of "Möbius transformation"
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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> | |
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. | ||
Revision as of 22:54, March 14, 2007
Möbius transformations are conformal, bilinear functions of the form
where , , and . It is an automorphism of the Riemann sphere, and the set of all Möbius transformations on the Riemann sphere forms the automorphism group.
