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  2. Reflection (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Reflection_(mathematics)

    In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis

  3. Householder transformation - Wikipedia

    en.wikipedia.org/wiki/Householder_transformation

    In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin. The Householder transformation was used in a 1958 paper by Alston Scott Householder. [1]

  4. Point reflection - Wikipedia

    en.wikipedia.org/wiki/Point_reflection

    In mathematics, reflection through the origin refers to the point reflection of Euclidean space R n across the origin of the Cartesian coordinate system. Reflection through the origin is an orthogonal transformation corresponding to scalar multiplication by − 1 {\displaystyle -1} , and can also be written as − I {\displaystyle -I} , where I ...

  5. Rotations and reflections in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotations_and_reflections...

    A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.

  6. Transformation (function) - Wikipedia

    en.wikipedia.org/wiki/Transformation_(function)

    In mathematics, a transformation, transform, or self-map [1] is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: XX. [2] [3] [4] Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific ...

  7. Glide reflection - Wikipedia

    en.wikipedia.org/wiki/Glide_reflection

    A glide reflection is the composition of a reflection across a line and a translation parallel to the line. This footprint trail has glide-reflection symmetry. Applying the glide reflection maps each left footprint into a right footprint and vice versa.

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  9. Orthogonal matrix - Wikipedia

    en.wikipedia.org/wiki/Orthogonal_matrix

    The special case of the reflection matrix with θ = 90° generates a reflection about the line at 45° given by y = x and therefore exchanges x and y; it is a permutation matrix, with a single 1 in each column and row (and otherwise 0): []. The identity is also a permutation matrix.