# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# ShearingMatrix

ShearingMatrix[θ,v,n]
gives the matrix corresponding to shearing by θ radians along the direction of the vector v, and normal to the vector n.

## DetailsDetails

• ShearingMatrix gives matrices corresponding to shearing with the origin kept fixed.
• ShearingMatrix gives matrices with determinant 1, corresponding to area- or volume-preserving transformations.
• In 2D, ShearingMatrix turns rectangles into parallelograms. ShearingMatrix[θ,{1,0},{0,1}] effectively slants by angle θ to the right.
• In 3D, ShearingMatrix does the analog of shearing a deck of cards by angle θ in the direction v, with the cards being oriented so as to have normal vector n.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

A shearing by θ radians along the axis:

 Out[1]//MatrixForm=

Apply a 30° shear along the axis to a square:

 Out[1]=