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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: : 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:'' : Similarly, if ''N'' is a submanifold or subvariety in ''M'', then the codimension of ''N'' in ''M'' is : 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 : 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
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