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・ Affine bundle
・ Affine cipher
・ Affine combination
・ Affine connection
・ Affine coordinate system
・ Affine curvature
・ Affine differential geometry
・ Affine focal set
・ Affine gauge theory
・ Affine geometry
・ Affine geometry of curves
・ Affine Grassmannian
・ Affine Grassmannian (manifold)
・ Affine group
・ Affine Hecke algebra
Affine hull
・ Affine involution
・ Affine Lie algebra
・ Affine logic
・ Affine manifold
・ Affine manifold (disambiguation)
・ Affine monoid
・ Affine plane
・ Affine plane (incidence geometry)
・ Affine pricing
・ Affine q-Krawtchouk polynomials
・ Affine representation
・ Affine root system
・ Affine shape adaptation
・ Affine space


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Affine hull : ウィキペディア英語版
Affine hull
In mathematics, the affine hull of a set ''S'' in Euclidean space R''n'' is the smallest affine set containing ''S'', or equivalently, the intersection of all affine sets containing ''S''. Here, an ''affine set'' may be defined as the translation of a vector subspace.
The affine hull aff(''S'') of ''S'' is the set of all affine combinations of elements of ''S'', that is,
:\operatorname (S)=\left\, \, \sum_^k \alpha_i=1 \right\}.
==Examples==

*The affine hull of a singleton (a set made of one single point) is the singleton itself.
*The affine hull of a set of two different points is the line through them.
*The affine hull of a set of three points not on one line is the plane going through them.
*The affine hull of a set of four points not in a plane in R''3'' is the entire space R''3''.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Affine hull」の詳細全文を読む



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