title: Affine
text: # Affine
  
  Affine may describe any of various topics concerned with connections or affinities.
  
  It may refer to:
  
  * Affine, a relative by marriage in law and anthropology
  * 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 Coordinate System, a coordinate system that can be viewed as a Cartesian coordinate system where the axes have been placed so that they are not necessarily orthogonal to each other. See tensor.
  * Affine differential geometry, a geometry that studies differential invariants under the action of the special affine group
  * Affine gap penalty, the most widely used scoring function used for sequence alignment, especially in bioinformatics
  * Affine geometry, a geometry characterized by parallel lines
  * Affine group, the group of all invertible affine transformations from any affine space over a field K into itself
  * Affine logic, a substructural logic whose proof theory rejects the structural rule of contraction
  * 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 morphism, a morphism of schemes such that the pre-image of an open affine subscheme is affine
  * Affine space, an abstract structure that generalises the affine-geometric properties of Euclidean space
  * Affine tensor, a tensor belonging to an affine coordinate system
  * Affine transformation, a transformation that preserves the relation of parallelism between lines
  