affine space wikipedia - EAS
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See all on Wikipediahttps://en.wikipedia.org/wiki/Affine_spaceIn 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 … See more
The following characterization may be easier to understand than the usual formal definition: an affine space is what is left of a vector space after one has forgotten which point is the origin (or, in the words of the French … See more
An affine space is a set A together with a vector space , and a transitive and free action of the additive group of on the set A. The elements of the … See more
Every vector space V may be considered as an affine space over itself. This means that every element of V may be considered either as a point or … See more
Let a1, ..., an be a collection of n points in an affine space, and be n elements of the ground field.
Suppose that . For any two points o and o' one has See more
Given two affine spaces A and B whose associated vector spaces are and , an affine map or affine homomorphism from A to B is a map
such that See moreDefinition of Euclidean spaces
Euclidean spaces (including the one-dimensional line, two-dimensional plane, and three … See more• When children find the answers to sums such as 4 + 3 or 4 − 2 by counting right or left on a number line, they are treating the number line as a one-dimensional affine space.
• The space of energies is an affine space for , since it is often not meaningful to talk about … See moreWikipedia text under CC-BY-SA license- https://en.wikipedia.org/wiki/Complex_affine_space
Affine geometry, broadly speaking, is the study of the geometrical properties of lines, planes, and their higher dimensional analogs, in which a notion of "parallel" is retained, but no metrical notions of distance or angle are. Affine spaces differ from linear spaces (that is, vector spaces) in that they do not have a distinguished choice of origin. So, in the words of Marcel Berger, "An affine space is nothing more than a vector space whose origin we try to forget about, by adding translations to th…
Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 9 mins
- https://en.wikipedia.org/wiki/Talk:Affine_space
- If ever there was a page that needed 'or in words' after its symbolic logic, this is it. What's that square ended right hand arrow? I believe that Wikipedia is intended to provide readable explanations, given a fair background. I have a fair background, but the assumption of the writers is that the symbols of set theory, as compared to logic as com...
- https://handwiki.org/wiki/Affine_space
- Definition of Euclidean spaces
Euclidean spaces (including the one-dimensional line, two-dimensional plane, and three-dimensional space commonly studied in elementary geometry, as well as higher-dimensional analogues) are affine spaces. Indeed, in most modern definitions, a Euclidean space is defined t… - Affine properties
In Euclidean geometry, the common phrase "affine property" refers to a property that can be proved in affine spaces, that is, it can be proved without using the quadratic form and its associated inner product. In other words, an affine property is a property that does not involve le…
- Definition of Euclidean spaces
- https://en.wikipedia.org/wiki/Affine_geometry
- In mathematics, affine geometry is what remains of Euclidean geometry when ignoring the metric notions of distance and angle. As the notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines. Therefore, Playfair's axiom is fundamental in affine geomet...
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- https://brilliant.org/wiki/affine-spaces
WebAn affine space is a triple (A, V, +) (A,V,+) where A A is a set of objects called points and V V is a vector space with the following properties: \forall a \in A, \vec {v}, \vec {w} \in V, a + …
- https://en.wikipedia.org/wiki/Exotic_affine_space
WebIn algebraic geometry, an exotic affine space is a complex algebraic variety that is diffeomorphic to for some n, but is not isomorphic as an algebraic variety to . [1] [2] [3] …
- https://en.wikipedia.org/wiki/Affine_transformation
WebIn Euclidean geometry, an affine transformation or affinity is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, an affine transformation …
Affine space - Wikipedia
https://static.hlt.bme.hu/semantics/external/pages...WebIn mathematics, an affine spaceis a geometric structurethat generalizes some of the properties of Euclidean spacesin such a way that these are independent of the concepts …
- https://en.wikipedia.org/wiki/Affine
WebAffine representation, a continuous group homomorphism whose values are automorphisms of an affine space; Affine scheme, the spectrum of prime ideals of a commutative ring …
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