Affine
Look up affine in Wiktionary, the free dictionary.
Affine may describe any of various topics concerned with connections or affinities. It is used in mathematics and applications with an unrelated meaning.
It may refer to:
- Affine, a relative by marriage in law and anthropology
Mathematics
In mathematics, affine is usually used to qualify topics where linear expressions may have constant terms and generaliztions of such topics.
- 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.
- Affine differential geometry, a geometry that studies differential invariants under the action of the special affine group
- 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 transformation, a transformation that preserves the relation of parallelism between lines
Mathematics applications
- Affine cipher, a special case of the more general substitution cipher
- Affine gap penalty, the most widely used scoring function used for sequence alignment, especially in bioinformatics