Reflections (mathematics)

URI: https://gptkb.org/entity/Reflections_(mathematics)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	Isometry Mathematical transformation
gptkbp:alsoKnownAs	gptkb:Mirror_symmetry
gptkbp:category	gptkb:Symmetry gptkb:Euclidean_geometry gptkb:Linear_algebra
gptkbp:fixedPoints	Points on the mirror (line or plane of reflection)
gptkbp:groupGeneratedByReflections	gptkb:Weyl_group
gptkbp:hasSpecialCase	Euclidean transformation Affine transformation Orthogonal transformation
https://www.w3.org/2000/01/rdf-schema#label	Reflections (mathematics)
gptkbp:in2D	Reflection across a line
gptkbp:in3D	Reflection across a plane
gptkbp:isInvolutive	True
gptkbp:isLinearTransformation	True
gptkbp:isOrientationReversing	True
gptkbp:matrixRepresentation	Orthogonal matrix with determinant -1
gptkbp:order	2
gptkbp:preserves	Angle Distance
gptkbp:relatedTo	gptkb:Symmetry Glide reflection Parity (physics) Rotation (mathematics) Translation (mathematics)
gptkbp:usedIn	gptkb:Computer_graphics gptkb:Physics gptkb:geometry gptkb:Crystallography gptkb:Group_theory
gptkbp:bfsParent	gptkb:Reflections
gptkbp:bfsLayer	5