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      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


      See also


      Affinity (disambiguation)

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    AFFiNE - All In One KnowledgeOS

    AFFiNE - All In One KnowledgeOS

    Contact Us - Affine

    Contact Us - Affine

    Affine Careers | Levels.fyi

    Affine Careers | Levels.fyi

    Best of JS • Affine

    Best of JS • Affine

    Affine Client — Made with Tauri

    Affine Client — Made with Tauri

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    AFFINE on Behance

    AFFINE on Behance

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    affine

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    What is the difference between linear and affine function?

    Jun 8, 2023 · A linear function fixes the origin, whereas an affine function need not do so. An affine function is the composition of a linear function with a translation, so while the linear part fixes the origin, the translation can map it somewhere else.

    intuition - What is the affine space and what is it for?

    For me affine spaces are useful mainly because of their affine transformations, that is of bijective transformations, preserving straight lines of the affine space. Affine thansformations of $\Bbb R^n$ are less rigid than motions, because we don’t required to keep distances. So, for instance, we can affinely transform a circle into an ellipse ...

    What is an Affine Span? - Mathematics Stack Exchange

    Sep 11, 2021 · According to this definition of affine spans from wikipedia, "In mathematics, the affine hull or affine span of a set S in Euclidean space Rn is the smallest affine set containing S, or equivalently, the intersection of all affine sets containing S." They give the definition that it is the set of all affine combinations of elements of S.

    what is the difference between linear transformation and affine ...

    Recently, I am struglling with the difference between linear transformation and affine transformation. Are they the same ? I found an interesting question on the difference between the functions. ...

    Understanding affine subsets - Mathematics Stack Exchange

    So, having the definition of an affine set, we can construct the appropriate parallel subspace. Of course ...

    linear algebra - What is the difference between linearly and …

    Jun 24, 2017 · To augment Lord Shark's answer, I just wanted to talk a little about the intuition behind it. Intuitively, a set of vectors is linearly dependent if there are more vectors than necessary to generate their span, i.e. the smallest subspace containing them.

    general topology - Why an affine morphism is separated?

    Feb 7, 2021 · $\begingroup$ yes. you use an implication, namely, that local on the target means that if I have the closed immersion property for an (open affine) cover then it holds globally. But local on the target has a slightly different definition, for instance check stacks.math.columbia.edu/tag/02KN .

    Is there any difference between a flat manifold and an affine space?

    $\begingroup$..on an affine space is the underlying vector space, which gives you the ability to add vectors to points and to perform affine combinations; this is something not available on a general Riemannian manifold. I do agree that you have a way to turn an affine space into a Riemannian manifold (by means of non canonical choices).

    Definition of an affine set - Mathematics Stack Exchange

    Note that the second definition is a generalisation of the first. A set is affine iff it contains all lines through any two points in the set (hence, as a trivial case, a set containing a single point is affine). (Thanks to @McFry who caught a little sloppiness in my original answer.)

    Definition of an affine subspace - Mathematics Stack Exchange

    I am reading this introduction to Mechanics and the definition it gives (just after Proposition 1.1.2) for an affine subspace puzzles me.