# LinearFractionalTransform

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 • LinearFractionalTransform gives a TransformationFunction that can be applied to vectors.
• For ordinary linear fractional transforms in n dimensions, m is an matrix.
• LinearFractionalTransform in general supports matrices for transformations in dimensions.
• In LinearFractionalTransform[{a,b,c,d}], a is a matrix, b and c are vectors, and d is a scalar.

# 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: