ReflectionMatrix [v]
gives the matrix that represents reflection of points in a mirror normal to the vector v.
ReflectionMatrix
ReflectionMatrix [v]
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
- ReflectionMatrix […,TargetStructure Automatic ] is equivalent to ReflectionMatrix […,TargetStructure "Dense"].
Examples
open all close allBasic 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 vectoror 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:
See Also
ReflectionTransform RotationMatrix OrthogonalMatrix UnitaryMatrix
Function Repository: RayTransferMatrix
Related Guides
Related Workflows
- Rotate, Pan and Zoom 3D Graphics
Text
Wolfram Research (2007), ReflectionMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/ReflectionMatrix.html (updated 2024).
CMS
Wolfram Language. 2007. "ReflectionMatrix." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. 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_2025_reflectionmatrix, author="Wolfram Research", title="{ReflectionMatrix}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ReflectionMatrix.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_reflectionmatrix, organization={Wolfram Research}, title={ReflectionMatrix}, year={2024}, url={https://reference.wolfram.com/language/ref/ReflectionMatrix.html}, note=[Accessed: 17-November-2025]}