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>
+
f(z) = (az + b)/(cz + d)
  
−
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 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.

Revision as of 22:56, March 14, 2007

Möbius transformations are conformal, bilinear functions of the form

f(z) = (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.

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