Examples for

Geometric Transformations
Geometric transformations are bijections preserving certain geometric properties, usually from the xy-plane to itself but can also be of higher dimension. In particular for each linear geometric transformation, there is one unique real matrix representation. Wolfram|Alpha has the ability to compute the transformation matrix for a specific 2D or 3D transformation activity or to return a general transformation calculator for rotations, reflections and shears.

Rotations

Compute the matrix of a rotation transform and visualize it.

Visualize a rotation and compute its matrix:

Visualize a rotation in 3D:

More examples

Reflections

Compute the matrix of a reflection transform and visualize it.

Visualize a reflection and compute its matrix:

Visualize a reflection in 3D:

More examples

Shears

Compute the matrix of a shear transform and visualize it.

Visualize a shear and compute its matrix:

Visualize a shear in 3D:

More examples