# ReflectionMatrix

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

# Details and Options

• The reflection is in a mirror that goes through the origin.
• ReflectionMatrix works in any number of dimensions. In 2D it reflects in a line; in 3D it reflects in a plane.
• ReflectionMatrix supports the option TargetStructure, which specifies the structure of the returned matrix. Possible settings for TargetStructure include:
•  Automatic automatically choose the representation returned "Dense" represent the matrix as a dense matrix "Orthogonal" represent the matrix as an orthogonal matrix "Unitary" represent the matrix as a unitary matrix
• is equivalent to ReflectionMatrix[,TargetStructure"Dense"].

# Examples

open allclose all

## Basic Examples(2)

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

Reflect along the vector or equivalently in the plane given by :

## Scope(4)

Reflect along the vector or equivalently in the plane given by :

Points in the reflection plane remain fixed:

Points outside the reflection plane get reflected in the plane:

Reflection matrix for symbolic unit vector {u,v}:

Vectors normal to {u,v} remain unchanged:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

## Options(1)

### TargetStructure(1)

Return the reflection matrix as a dense matrix:

Return the reflection matrix as an orthogonal matrix:

Return the reflection matrix as a unitary matrix:

## Applications(1)

Flipping a surface:

## Properties & Relations(3)

The determinant of a reflection matrix is :

The inverse of a reflection matrix is the matrix itself:

Reflection can be thought of as a special case of scaling:

## Possible Issues(1)

Reflection changes the orientation of polygons:

## Neat Examples(1)

Reflections of a cuboid in vertical planes:

Wolfram Research (2007), ReflectionMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/ReflectionMatrix.html (updated 2023).

#### Text

Wolfram Research (2007), ReflectionMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/ReflectionMatrix.html (updated 2023).

#### CMS

Wolfram Language. 2007. "ReflectionMatrix." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/ReflectionMatrix.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_reflectionmatrix, author="Wolfram Research", title="{ReflectionMatrix}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/ReflectionMatrix.html}", note=[Accessed: 23-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_reflectionmatrix, organization={Wolfram Research}, title={ReflectionMatrix}, year={2023}, url={https://reference.wolfram.com/language/ref/ReflectionMatrix.html}, note=[Accessed: 23-June-2024 ]}