Affine
Encyclopedia
Affine may refer to:
- Affine cipherAffine cipherThe affine cipher is a type of monoalphabetic substitution cipher, wherein each letter in an alphabet is mapped to its numeric equivalent, encrypted using a simple mathematical function, and converted back to a letter...
, a special case of the more general substitution cipher - Affine combination, a certain kind of constrained linear combination
- Affine connectionAffine connectionIn the branch of mathematics called differential geometry, an affine connection is a geometrical object on a smooth manifold which connects nearby tangent spaces, and so permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space...
, a connection on the tangent bundle of a differentiable manifold - Affine geometryAffine geometryIn mathematics affine geometry is the study of geometric properties which remain unchanged by affine transformations, i.e. non-singular linear transformations and translations...
, a geometry not involving any notions of origin, length or angle - Affine differential geometryAffine differential geometryAffine differential geometry, is a type of differential geometry in which the differential invariants are invariant under volume-preserving affine transformations. The name affine differential geometry follows from Klein's Erlangen program...
, a geometry that studies differential invariants under the action of the special affine group - Affine groupAffine groupIn 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 quaternions....
, the group of all invertible affine transformations from any affine space over a field K into itself - Affine representationAffine representationAn affine representation of a topological group G on an affine space A is a continuous group homomorphism from G to the automorphism group of A, the affine group Aff...
, a continuous group homomorphism whose values are automorphisms of an affine space - Affine scheme, the spectrum of prime ideals of a commutative ring
- Affine (Société), A French Commercial real estate company.
- Affine spaceAffine spaceIn mathematics, an affine space is a geometric structure that generalizes the affine 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 cannot add points. In particular, there is no distinguished point...
, an abstract structure that generalises the affine-geometric properties of Euclidean space - Affine transformationAffine transformationIn geometry, an affine transformation or affine map or an affinity is a transformation which preserves straight lines. It is the most general class of transformations with this property...
, a linear transformation followed by a translation between two vector spaces, or equivalently, a transformation that preserves all affine combinations