# TransformationMatrix

TransformationMatrix[tfun]

gives the homogeneous matrix associated with a TransformationFunction object.

# Details

• 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.

# Examples

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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:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_transformationmatrix, author="Wolfram Research", title="{TransformationMatrix}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/TransformationMatrix.html}", note=[Accessed: 24-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_transformationmatrix, organization={Wolfram Research}, title={TransformationMatrix}, year={2007}, url={https://reference.wolfram.com/language/ref/TransformationMatrix.html}, note=[Accessed: 24-May-2024 ]}