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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 of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments. Affine space is the setting for affine geometry.

Affine algebraic geometry, Examples & Coordinates

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Overview

Informal description

Definition

Affine subspaces and parallelism

Affine map

Vector spaces as affine spaces

Relation to Euclidean spaces

Affine combinations and barycenter

Examples

Affine span and bases

Coordinates

Properties of affine homomorphisms

Axioms

Relation to projective spaces

Affine algebraic geometry

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Map overview Semantic statistics

Affine space

Nodes205
Edges204
Triples173
Avg. degree1.99
Density0.009756
Components1

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Affine space

Top relations

related to References · 45
Affine space → Affine, Affine Differential Geometry, Affine Maps, Agustí, Algebraic Geometry, Berger, Berlin, Cambridge University Press, Dover, Dover Publications, EMS PressHartshorne, Encyclopedia, Ernst, Euclidean Motions, Geometry, Harold Scott MacDonald, Introduction, ISBN, John Wiley, London
related to Examples · 16
Affine space → Addition, Any, End, Euclidean, Generalizing, Hom, In, Ker, Physical, Specific, That, The, Time, To, Tx, W/V
related to Informal description · 10
Affine space → Alice, An, Bob, French, However, Imagine, Marcel Berger, Similarly, The, Two
related to Cohomology · 8
Affine space → But, In, Like, More, Quillen, Serre's, Suslin, This
related to Zariski topology · 8
Affine space → Affine, As, In, The Zariski, There, This, When, Zariski
related to Relation to projective spaces · 7
Affine space → Affine, Conversely, For, Further, Möbius, Riemann, Similar
see also · 7
Affine space → Affine, Coordinate, Curvilinear, Geometry, Mathematical, Real, Smallest
is a · 6
Affine space → generating set that is also independent, 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, principal homogeneous space for the action of the additive group of a vector space, set A together with a vector space A, set of the common zeros of the zero polynomial, setting for affine geometry.As in Euclidean space
related to Affine algebraic geometry · 6
Affine space → As, For, In, The, Then, This
related to Definition · 6
Affine space → An, Axioms, Euclid's Elements, Euclidean, The, While

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Important terminology

affine space vector displaystyle point points linear coordinates subspace spaces origin one associated set dimension overrightarrow defined may called geometry

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Affine spaceis ageometric 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 angles0.90text
Affine spaceis asetting for affine geometry.As in Euclidean space0.90text
Affine spaceis aset A together with a vector space A0.90text
Affine spaceis aprincipal homogeneous space for the action of the additive group of a vector space0.90text
Affine spaceis agenerating set that is also independent0.90text
Affine spaceis aset of the common zeros of the zero polynomial0.90text
Affine spacerelated to Affine algebraic geometryIn0.60section
Affine spacerelated to Affine algebraic geometryFor0.60section
Affine spacerelated to Affine algebraic geometryThen0.60section
Affine spacerelated to Affine algebraic geometryAs0.60section
Affine spacerelated to Affine algebraic geometryThe0.60section
Affine spacerelated to Affine algebraic geometryThis0.60section

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    Min side: 3
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