Difference between revisions of "Möbius transformation"

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Möbius transformations are conformal, bilinear functions of the form
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Möbius transformations are conformal, [[bilinear function]]s of the form
  
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:<math>t = f(z) = \frac{az + b}{cz + d},</math>
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:<math>f(z) = \frac{a z + b}{c z + d}</math>
  
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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.
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where a, b, c, d are real numbers, and ''ad'' &minus; ''bc'' &ne; 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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[[Category:Complex Analysis]]

Latest revision as of 01:02, August 14, 2018

Möbius transformations are conformal, bilinear functions of the form

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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