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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク General position ： ウィキペディア英語版 General position In algebraic geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the ''general case'' situation, as opposed to some more special or coincidental cases that are possible, which is referred to as special position. Its precise meaning differs in different settings. For example, generically, two lines in the plane intersect in a single point (they are not parallel or coincident). One also says "two generic lines intersect in a point", which is formalized by the notion of a generic point. Similarly, three generic points in the plane are not collinear; if three points are collinear (even stronger, if two coincide), this is a degenerate case. This notion is important in mathematics and its applications, because degenerate cases may require an exceptional treatment; for example, when stating general theorems or giving precise statements thereof, and when writing computer programs (see ''generic complexity''). ==General linear position== A set of at least $d+1$ points in $d$-dimensional affine space ($d$-dimensional Euclidean space is a common example) is said to be in general linear position (or just general position) if no hyperplane contains more than $d$ points — ''i.e.'' the points do not satisfy any more linear relations than they must. In more generality, a set containing $k$ points, for arbitrary $k$, is in general linear position if and only if no $(k-2)$-dimensional flat contains all $k$ points. A set of at most $d\; +\; 1$ points in general linear position is also said to be ''affinely independent'' (this is the affine analog of linear independence of vectors, or more precisely of maximal rank), and $d+1$ points in general linear position in affine ''d''-space are an affine basis. See affine transformation for more. Similarly, ''n'' vectors in an ''n''-dimensional vector space are linearly independent if and only if the points they define in projective space (of dimension $n-1$) are in general linear position. If a set of points is not in general linear position, it is called a degenerate case or degenerate configuration, which implies that they satisfy a linear relation that need not always hold. A fundamental application is that, in the plane, five points determine a conic, as long as the points are in general linear position (no three are collinear). 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「General position」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.