- hyperplane reflection
- мат.отражение относительно гиперплоскости
English-Russian scientific dictionary. 2008.
hyperplane reflection
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Reflection (mathematics) — This article is about reflection in geometry. For reflexivity of binary relations, see reflexive relation. A reflection through an axis followed by a reflection across a second axis parallel to the first one results in a total motion which is a… … Wikipedia
Reflection (linear algebra) — In linear algebra, a reflection is a linear transformation that squares to the identity ( R 2 = I , where R is in K dimensional space), also known as an involution in the general linear group. In addition to reflections across hyperplanes, the… … Wikipedia
Reflection group — A reflection group is a group action, acting on a finite dimensional vector space, which is generated by reflections: elements that fix a hyperplane in space pointwise.For example, with regard to ordinary reflections in planes in 3D, a reflection … Wikipedia
Complex reflection group — In mathematics, a complex reflection group is a group acting on a finite dimensional complex vector space, that is generated by complex reflections: non trivial elements that fix a complex hyperplane in space pointwise. (Complex reflections are… … Wikipedia
Oblique reflection — In Euclidean geometry, oblique reflections generalize ordinary reflections by not requiring that reflection be done using perpendiculars. If two points are oblique reflections of each other, they will still stay so under affine transformations.… … Wikipedia
Root system — This article discusses root systems in mathematics. For root systems of plants, see root. Lie groups … Wikipedia
Surface normal — Normal vector redirects here. For a normalized vector, or vector of length one, see unit vector. A polygon and two of its normal vectors … Wikipedia
Householder transformation — In mathematics, a Householder transformation in 3 dimensional space is the reflection of a vector in a plane. In general Euclidean space it is a linear transformation that describes a reflection in a hyperplane (containing the origin).The… … Wikipedia
Coxeter–Dynkin diagram — See also: Dynkin diagram Coxeter Dynkin diagrams for the fundamental finite Coxeter groups … Wikipedia
Möbius transformation — Not to be confused with Möbius transform or Möbius function. In geometry, a Möbius transformation of the plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − … Wikipedia
Orthogonal matrix — In linear algebra, an orthogonal matrix (less commonly called orthonormal matrix[1]), is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors). Equivalently, a matrix Q is orthogonal if… … Wikipedia
