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In linear algebra and functional analysis, the kernel (also null space or nullspace) of a linear map between two vector spaces ''V'' and ''W'', is the set of all elements v of ''V'' for which , where 0 denotes the zero vector in ''W''. That is, in set-builder notation, : ==Properties of the Kernel== The kernel of ''L'' is a linear subspace of the domain ''V''.〔Linear algebra, as discussed in this article, is a very well established mathematical discipline for which there are many sources. Almost all of the material in this article can be found in Lay 2005, Meyer 2001, and Strang 2005.〕 In the linear map , two elements of ''V'' have the same image in ''W'' if and only if their difference lies in the kernel of ''L'': : It follows that the image of ''L'' is isomorphic to the quotient of ''V'' by the kernel: : This implies the rank–nullity theorem: : where, by “rank” we mean the dimension of the image of ''L'', and by “nullity” that of the kernel of ''L''. When ''V'' is an inner product space, the quotient can be identified with the orthogonal complement in ''V'' of ker(''L''). This is the generalization to linear operators of the row space, or coimage, of a matrix. 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「Kernel (linear algebra)」の詳細全文を読む スポンサード リンク
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