affine space

аффинное пространство

Авиасловарь. . 2004.

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  • Affine space — In mathematics, an affine space is an abstract structure that generalises the affine geometric properties of Euclidean space. In an affine space, one can subtract points to get vectors, or add a vector to a point to get another point, but one… …   Wikipedia

  • affine space — noun a vector space having no origin …   Wiktionary

  • 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

  • Affine — may refer to:*Affine cipher, a special case of the more general substitution cipher *Affine combination, a certain kind of constrained linear combination *Affine connection, a connection on the tangent bundle of a differentiable manifold *Affine… …   Wikipedia

  • Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… …   Wikipedia

  • Space group — In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains. In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered… …   Wikipedia

  • Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… …   Wikipedia

  • Affine transformation — In geometry, an affine transformation or affine map or an affinity (from the Latin, affinis , connected with ) between two vector spaces (strictly speaking, two affine spaces) consists of a linear transformation followed by a translation::x… …   Wikipedia

  • Affine group — In mathematics, the affine group or general affine group of any affine space over a field K is the group of all invertible affine transformations from the space into itself.It is a Lie group if K is the real or complex field or… …   Wikipedia

  • Affine geometry of curves — In the mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties of such curves which are invariant under the special affine group In the classical… …   Wikipedia

  • Affine representation — An affine representation of a topological (Lie) group G on an affine space A is a continuous (smooth) group homomorphism from G to the automorphism group of A , the affine group Aff( A ). Similarly, an affine representation of a Lie algebra g on… …   Wikipedia

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