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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).
  • For ordinary linear fractional transforms in n dimensions, m is an (n+1)x(n+1) matrix.
EXAMPLESCLOSE ALL
Basic Examples   (1)
This creates the linear fractional transform (a.x+b)/(c.x+d):
This is the corresponding formula:
This creates the linear fractional transform (a.x+b)/(c.x+d):
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In[2]:=
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Out[2]=
This is the corresponding formula:
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Out[3]=
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:
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