翻訳と辞書 Words near each other ・ Codicia ・ Codicil ・ Codicil (will) ・ Codicology ・ Codicote ・ Codicote F.C. ・ Codie award ・ Codie Prevost ・ Codie Taylor ・ Codification ・ Codification (law) ・ Codification (linguistics) ・ Codigo Emprende ・ Codigoro ・ Codilla ・ Codimension ・ Codinaeopsin ・ Codine ・ Coding ・ Coding (social sciences) ・ Coding (therapy) ・ Coding Accuracy Support System ・ Coding Analysis Toolkit ・ Coding by exception ・ Coding conventions ・ Coding gain ・ Coding region ・ Coding strand ・ Coding Technologies ・ Coding theory Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Codimension ： ウィキペディア英語版 Codimension In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties. The dual concept is relative dimension. ==Definition== Codimension is a ''relative'' concept: it is only defined for one object ''inside'' another. There is no “codimension of a vector space (in isolation)”, only the codimension of a vector ''sub''space. If ''W'' is a linear subspace of a finite-dimensional vector space ''V'', then the codimension of ''W'' in ''V'' is the difference between the dimensions: :$\backslash operatorname(W)\; =\; \backslash dim(V)\; -\; \backslash dim(W).$ It is the complement of the dimension of ''W,'' in that, with the dimension of ''W,'' it adds up to the dimension of the ambient space ''V:'' :$\backslash dim(W)\; +\; \backslash operatorname(W)\; =\; \backslash dim(V).$ Similarly, if ''N'' is a submanifold or subvariety in ''M'', then the codimension of ''N'' in ''M'' is :$\backslash operatorname(N)\; =\; \backslash dim(M)\; -\; \backslash dim(N).$ Just as the dimension of a submanifold is the dimension of the tangent bundle (the number of dimensions that you can move ''on'' the submanifold), the codimension is the dimension of the normal bundle (the number of dimensions you can move ''off'' the submanifold). More generally, if ''W'' is a linear subspace of a (possibly infinite dimensional) vector space ''V'' then the codimension of ''W'' in ''V'' is the dimension (possibly infinite) of the quotient space ''V''/''W'', which is more abstractly known as the cokernel of the inclusion. For finite-dimensional vector spaces, this agrees with the previous definition :$\backslash operatorname(W)\; =\; \backslash dim(V/W)\; =\; \backslash dim\; \backslash operatorname\; (\; W\; \backslash to\; V\; )\; =\; \backslash dim(V)\; -\; \backslash dim(W),$ and is dual to the relative dimension as the dimension of the kernel. Finite-codimensional subspaces of infinite-dimensional spaces are often useful in the study of topological vector spaces. 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「Codimension」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.