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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 : where each is a vector space. For a given ''n'' the elements of 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
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