# Affine

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 geometry, a geometry characterized by parallel lines
• Affine differential geometry, a geometry that studies differential invariants under the action of the special affine group
• Affine group, the group of all invertible affine transformations from any affine space over a field K into itself
• Affine representation, 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 space, an abstract structure that generalises the affine-geometric properties of Euclidean space
• Affine transformation, a linear transformation that preserves the relation of parallelism between lines

### Other articles related to "affine":

Special Affine Group
... In the mathematical study of transformation groups, the special affine group is the group of affine transformations of a fixed affine space which preserve volume ... This is the affine analogue of the special linear group ... On Rn, every special affine transformation has the form where A is an n×n matrix of determinant one, and b is a fixed vector in Rn ...
Affine Focal Set - Local Structure
... up to local diffeomorphism, the affine focal set ... If the family of affine distance functions can be shown to be a certain kind of family then the local structure is known ... We want the family of affine distance functions to be a versal unfolding of the singularities which arrise ...
Abstract Algebraic Variety - Introduction and Definitions - Affine Varieties
... Let k be an algebraically closed field and let An be an affine n-space over k ... vanish, that is to say A subset V of An is called an affine algebraic set if V = Z(S) for some S ... A nonempty affine algebraic set V is called irreducible if it cannot be written as the union of two proper algebraic subsets ...
Linear Type System - Different Substructural Type Systems - Affine Type Systems
... Affine types are a weaker version of linear types and correspond to affine logic an affine resource can only be used once, while a linear one must be used once ...