Reflection (mathematics) - Definition and Overview

In mathematics, reflection (also spelt reflexion) refers to 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 is not unique, for example. Also, an inversion in inversive geometry is considered a reflection by this definition.

In algebra, especially relational algebra, a relation R is reflexive if, for any x,

x R x

E.g. equality is reflexive because

x = x.

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

• Coordinate rotations and reflections.