LinearFractionalTransform

LinearFractionalTransform[m] gives a TransformationFunction that represents a linear fractional transformation defined by the homogeneous matrix m.

• LinearFractionalTransform[{a, b, c, d}] represents a linear fractional transformation that maps r to (a.r+b)/(c.r+d).

Examples

Simple transformation:

LinearFractionalTransform[{{1, 2}, {0, 1}}][x]

Möbius transformation:

LinearFractionalTransform[{1, 0, 1, 1}][z]
(* z/(z + 1) *)

Apply to a point:

LinearFractionalTransform[{{2, 1}, {1, 1}}][{3}]

Please visit the official Wolfram Language Reference for more details.