Möbius transformations

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Möbius transformations

[′mər·bē·əs ‚tranz·fər′mā·shənz]
(mathematics)
These are the most commonly used conformal mappings of the complex plane; their form is ƒ(z) = (az + b)/(cz + d) where the real numbers a, b, c, and d satisfy ad-bc ≠ 0. Also known as linear fractional transformations. Also known as bilinear transformations; homographic transformations.
References in periodicals archive ?
It follows that [Mathematical Expression Omitted] is the restriction of a Mobius transformation, and the Corollary follows.
1] with a Mobius transformation, if necessary, we assume that in [Mathematical Expression Omitted] there is an annulus E bounded by the curves [f.
AhB], [LV]) that such a map exists and is unique up to post-compositions with Mobius transformations.
It follows that up to post-compositions with Mobius transformations, f = [f.
Conservation laws in physics can be related to Mobius transformations in both discrete and continuous spaces.
In the limit when the node spacing approaches zero, the continuous approximation appears and the Mobius transformations include the continuous symmetry transformations.