gives the homogeneous matrix associated with a TransformationFunction object.


  • For transformations in n dimensions, TransformationMatrix normally gives an × matrix.
  • mat[[1;;n,1;;n]] gives the linear part of the transformation; mat[[1;;n,-1]] gives the displacement vector.


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Basic Examples  (1)

Here is defined to be a rotation around the axis:

Get the transformation matrix:

The linear part:

The displacement vector:

Scope  (1)

Translation matrix in four dimensions:

Transformation of homogeneous coordinates:

Points at infinity do not change under translation:

Properties & Relations  (1)

The matrix of a general 2D affine transform:

Composition of linear fractional transformations corresponds to the product of their matrices:

Introduced in 2007