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Mathematica > Geometric Transforms >

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ReflectionMatrix

ReflectionMatrix[v]
gives the matrix that represents reflection of points in a mirror normal to the vector v.

ReflectionMatrix works in any number of dimensions. In 2D it reflects in a line; in 3D in a plane.

Reflect along the x axis, or equivalently reflect in the y axis:

Out[1]//MatrixForm=

Reflect along the vector

or equivalently in the plane given by

Out[1]//MatrixForm=