This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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Geometric Transforms
Mathematica's symbolic architecture and sophisticated mathematical capabilities allow it to take a uniquely high-level approach to geometric transformations—supporting complete geometric, matrix, and functional representations in any number of dimensions, whether for mechanical systems, computer graphics, or pure mathematics.
Geometric Object Transformations
Rotate  ▪ Translate  ▪ Scale
GeometricTransformation apply any transformation function to geometric objects
Transformation Matrices
RotationMatrix rotations in any number of dimensions
ScalingMatrix stretch or shrink along any direction
TransformationMatrix the matrix representation of a transformation function
Symbolic Transformation Functions
TransformationFunction general symbolic representation of transformations
Composition symbolic composition of transformation functions
InverseFunction inverse of transformation functions
Algebraic Structure
FiniteGroupData properties of finite groups