affine subspace
1Affine 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… …
2Affine 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… …
3Affine 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… …
4Affine 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… …
5Affine combination — In mathematics, an affine combination of vectors x 1, ..., x n is vector : sum {i=1}^{n}{alpha {i} cdot x {i = alpha {1} x {1} + alpha {2} x {2} + cdots +alpha {n} x {n}, called the linear combination of x 1, ..., x n , in which the sum of the… …
6Affine hull — In mathematics, the affine hull of a set S in Euclidean space R n is the smallest affine set containing S , or equivalently, the intersection of all affine sets containing S . Here, an affine set may be defined as the translation of a vector… …
7Affine Grassmannian (manifold) — In mathematics, there are two distinct meanings of the term affine Grassmannian . In one it is the manifold of all k dimensional affine subspaces of R n (described on this page), while in the other the Affine Grassmannian is a quotient of a group …
8Vector 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… …
9Hyperplane 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 …
10Hyperplane — 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… …
