affine property wikipedia - EAS
- 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 of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.
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See all on Wikipediahttps://en.wikipedia.org/wiki/Affine_transformationIn Euclidean geometry, an affine transformation, or an affinity (from the Latin, affinis, "connected with"), is a geometric transformation that preserves lines and parallelism (but not necessarily distances and angles). More generally, an affine transformation is an automorphism of an affine space (Euclidean
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See moreLet (X, V, k) be an affine space of dimension at least two, with X the point set and V the associated vector space over the field k. A semiaffine transformation f of X is a bijection of X onto itself satisfying:
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See moreAs shown above, an affine map is the composition of two functions: a translation and a linear map. Ordinary vector algebra uses matrix multiplication to represent linear maps, and vector addition to represent translations. Formally, in the finite-dimensional case, if
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See moreAn affine map between two affine spaces is a map on the points that acts linearly on the vectors (that is, the vectors between points of the space). In symbols, determines a linear transformation such that, for any pair of points :
or...
See moreIn their applications to digital image processing, the affine transformations are analogous to printing on a sheet of rubber and stretching the sheet's edges parallel to the plane. This transform
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See moreBy the definition of an affine space, V acts on X, so that, for every pair (x, v) in X × V there is associated a point y in X. We can denote this action by v→(x) = y. Here we use the convention that v→ = v are two interchangeable notations for an element of V. By fixing a point c in
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See moreProperties preserved
An affine transformation preserves:
1. collinearity between points: three or more points which lie on the...
See moreThe word "affine" as a mathematical term is defined in connection with tangents to curves in Euler's 1748 Introductio in analysin infinitorum. Felix Klein attributes the term "affine
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See moreWikipedia text under CC-BY-SA license- https://en.wikipedia.org/wiki/Affine_geometry
In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance …
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- https://en.wikipedia.org/wiki/Affine
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 …
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- https://en.wikipedia.org/wiki/Affine_space
In algebraic geometry, an affine variety (or, more generally, an affine algebraic set) is defined as the subset of an affine space that is the set of the common zeros of a set of so-called polynomial functions over the affine space. For defining a polynomial function over the affine space, one has to choose an affine frame. Then, a polynomial function is a function such that the image of any point is the value of some multivariate polynomial function of the coordinates of the point. As a c…
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