Category:Möbius Transformations

This category contains results about Möbius Transformations.
Definitions specific to this category can be found in Definitions/Möbius Transformations.

A Möbius transformation is a mapping $f: \overline \C \to \overline \C$ of the form:

$\map f z = \dfrac {a z + b} {c z + d}$

where:

$\overline \C$ denotes the extended complex plane

$a, b, c, d \in \C$ such that $a d - b c \ne 0$

We define:

$\map f {-\dfrac d c} = \infty$

if $c \ne 0$, and:

$\map f \infty = \begin{cases} \dfrac a c & : c \ne 0 \\ \infty & : c = 0 \end{cases}$