affine hyperplane

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• Hyperplane — A hyperplane is a concept in geometry. It is a higher dimensional generalization of the concepts of a line in Euclidean plane geometry and a plane in 3 dimensional Euclidean geometry. The most familiar kinds of hyperplane are affine and linear… …   Wikipedia

• Affine geometry — is a form of geometry featuring the unique parallel line property (see the parallel postulate) but where the notion of angle is undefined and lengths cannot be compared in different directions (that is, Euclid s third and fourth postulates are… …   Wikipedia

• Hyperplane at infinity — In mathematics, in particular projective geometry, the hyperplane at infinity, also called the ideal hyperplane, is an ( n −1) dimensional projective space added to an n dimensional affine space A, such as the real affine n space mathbb{R}^n , in …   Wikipedia

• Affine involution — In Euclidean geometry, of special interest are involutions which are linear or affine transformations over the Euclidean space R n . Such involutions are easy to characterize and they can be described geometrically.Linear involutionsTo give a… …   Wikipedia

• hyperplane — noun An n dimensional generalization of a plane; an affine subspace of dimension n 1 that splits an n dimensional space. (In a one dimensional space, it is a point; In two dimensional space it is a line; In three dimensional space, it is an… …   Wiktionary

• Lefschetz hyperplane theorem — In mathematics, the Lefschetz hyperplane theorem states that a hyperplane section W of a non singular complex algebraic variety V , in complex projective space, inherits most of its algebraic topology from V . This allows certain geometrical… …   Wikipedia

• Convex cone — In linear algebra, a convex cone is a subset of a vector space over an ordered field that is closed under linear combinations with positive coefficients. A convex cone (light blue). Inside of it, the light red convex cone consists of all points… …   Wikipedia

• 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

• Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

• Simplex — For other uses, see Simplex (disambiguation). A regular 3 simplex or tetrahedron In geometry, a simplex (plural simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n… …   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