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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 Graded vector space ： ウィキペディア英語版 Graded vector space In mathematics, a graded vector space is a vector space that has the extra structure of a ''grading'' or a ''gradation'', which is a decomposition of the vector space into a direct sum of vector subspaces. ==ℕ-graded vector spaces== Let ℕ be the set of non-negative integers. An ℕ-graded vector space, often called simply a graded vector space without the prefix ℕ, is a vector space ''V'' which decomposes into a direct sum of the form : $V\; =\; \backslash bigoplus\_\{n\; \backslash in\; \backslash mathbb\{N\}\}\; V\_n$ where each $V\_n$ is a vector space. For a given ''n'' the elements of $V\_n$ are then called homogeneous elements of degree ''n''. Graded vector spaces are common. For example the set of all polynomials in one or several variables forms a graded vector space, where the homogeneous elements of degree ''n'' are exactly the linear combinations of monomials of degree ''n''. 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「Graded vector space」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.