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In mathematics, the dimension of a vector space ''V'' is the cardinality (i.e. the number of vectors) of a basis of ''V'' over its base field. For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined. We say ''V'' is finite-dimensional if the dimension of ''V'' is finite, and infinite-dimensional if its dimension is infinite. The dimension of the vector space ''V'' over the field ''F'' can be written as dim''F''(''V'') or as (: F ), read "dimension of ''V'' over ''F''". When ''F'' can be inferred from context, dim(''V'') is typically written. == Examples == The vector space R3 has : as a basis, and therefore we have dimR(R3) = 3. More generally, dimR(R''n'') = ''n'', and even more generally, dim''F''(''F''''n'') = ''n'' for any field ''F''. The complex numbers C are both a real and complex vector space; we have dimR(C) = 2 and dimC(C) = 1. So the dimension depends on the base field. The only vector space with dimension 0 is , the vector space consisting only of its zero element. 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「Dimension (vector space)」の詳細全文を読む スポンサード リンク
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