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 | ||
| − | f(z) = | + | :<math>f(z) = \frac{a z + b}{c z + d}</math> |
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. | 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. | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 10:15, March 27, 2007
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.