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 to .

Details

Examples

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Basic Examples  (1)

This creates the linear fractional transform :

This is the corresponding formula:

Scope  (3)

If the scalar d is omitted, it is taken to be 1:

A single matrix is taken to be the homogeneous representation of the transform:

Suppose you have a linear fractional transform t:

The inverse is computed by applying InverseFunction:

This shows that s and t are inverses:

This shows the same thing using formulas:

Wolfram Research (2007), LinearFractionalTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/LinearFractionalTransform.html.

Text

Wolfram Research (2007), LinearFractionalTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/LinearFractionalTransform.html.

CMS

Wolfram Language. 2007. "LinearFractionalTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LinearFractionalTransform.html.

APA

Wolfram Language. (2007). LinearFractionalTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LinearFractionalTransform.html

BibTeX

@misc{reference.wolfram_2025_linearfractionaltransform, author="Wolfram Research", title="{LinearFractionalTransform}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/LinearFractionalTransform.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_linearfractionaltransform, organization={Wolfram Research}, title={LinearFractionalTransform}, year={2007}, url={https://reference.wolfram.com/language/ref/LinearFractionalTransform.html}, note=[Accessed: 21-February-2025 ]}