Difference between revisions of "Möbius transformation"
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:<math>f(z) = \frac{a z + b}{c z + d}</math> | :<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 10:17, 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.