Reflection (mathematics)
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- This article is about reflection in geometry. For reflexivity of binary relations, see reflexive relation.
In mathematics, a reflection (also spelt reflexion) is to invert a geometric figure, respect to a line or plane (but not a point). So for example, a reflection of a small English letter p, respect to the vertical line, would look like q. Reflection preserves the distance, and the operation is thus said to be isometric.
More formally, a reflection can be defined as an involutive automorphism of a space which leaves invariant a subspace of codimension 1. (This means that a two-dimensional (n dimensional) space is flipped around a one-dimensional (n-1 dimensional) axis within that space.)
Note that this applies to more than just Euclidean geometry. Reflections in affine geometry with respect to a given hyperplane are not unique, for example. Also, an inversion in inversive geometry is considered a reflection by this definition.
In LAPACK the term reflector with the types block reflector and elementary reflector is used to describe the functionality of the routines that implement the Householder transformation
See also
External link
- Reflection in Line (http://www.cut-the-knot.org/Curriculum/Geometry/Reflection.shtml) (requires Java)