Look up affine in Wiktionary, the free dictionary.
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
Look up affine in Wiktionary, the free dictionary. Affine may describe any of various topics concerned with connections or affinities. It may refer to:...
affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space...
In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent...
] . {\displaystyle k[X_{1},\ldots ,X_{n}].} An affine variety or affine algebraic variety, is an affine algebraic set such that the ideal generated by...
In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector...
In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...
Affine logic is a substructural logic whose proof theory rejects the structural rule of contraction. It can also be characterized as linear logic with...
In mathematics, an affine representation of a topological Lie group G on an affine space A is a continuous (smooth) group homomorphism from G to the automorphism...
The affine cipher is a type of monoalphabetic substitution cipher, where each letter in an alphabet is mapped to its numeric equivalent, encrypted using...
Exacum affine, known commercially as the Persian violet, is a species of plant in the family Gentianaceae. It is endemic to Socotra, part of Yemen, though...
differential geometry, an affine sphere is a hypersurface for which the affine normals all intersect in a single point. The term affine sphere is used because...
not distinct) in the complex affine space. Therefore, most of algebraic geometry is built in complex affine spaces and affine spaces over algebraically closed...
irreducible affine algebraic set is also called an affine variety.: 3 (Some authors use the phrase affine variety to refer to any affine algebraic set...
embedded in an ambient space of dimension n, generally a Euclidean space, an affine space or a projective space. Hypersurfaces share, with surfaces in a three-dimensional...
In mathematics, an affine combination of x1, ..., xn is a linear combination ∑ i = 1 n α i ⋅ x i = α 1 x 1 + α 2 x 2 + ⋯ + α n x n , {\displaystyle \sum...
affine Lie algebra, one can also form the associated affine Kac-Moody algebra, as described below. From a purely mathematical point of view, affine Lie...
linear transformations on the n+1-dimensional space Rn+1. These include both affine transformations (such as translation) and projective transformations. For...
neither weakening nor contraction): Every variable is used exactly once. Affine type systems (allow exchange and weakening, but not contraction): Every...
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in...
In geometry, an affine plane is a two-dimensional affine space. Typical examples of affine planes are Euclidean planes, which are affine planes over the...
Affine algebra may refer to: Affine Lie algebra, a type of Kac–Moody algebras The Lie algebra of the affine group Finitely-generated algebra Affine Hecke...
having vanishing geodesic curvature. More generally, in the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain...
In economics, affine pricing is a situation where buying more than zero of a good gains a fixed benefit or cost, and each purchase after that gains a per-unit...
isomorphic to one of this form is called an affine scheme. General schemes are obtained by gluing affine schemes together. Similarly, for a module M over...
the spherical and cylindrical coordinates for three-dimensional space. An affine line with a chosen Cartesian coordinate system is called a number line....
an affine variety to A1, we can define regular maps from one affine variety to another. First we will define a regular map from a variety into affine space:...
each of which the function is an affine function. (Thus "piecewise linear" is actually defined to mean "piecewise affine".) If the domain of the function...
properties from Euclidean space are no longer relevant. For example, in affine space, there is no concept of distance, so there are no reflections or motions...
mathematics, an affine braid group is a braid group associated to an affine Coxeter system. Their group rings have quotients called affine Hecke algebras...
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