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In the mathematical subfield of linear algebra or more generally functional analysis, the linear span (also called the linear hull) of a set of vectors in a vector space is the intersection of all subspaces containing that set. The linear span of a set of vectors is therefore a vector space. ==Definition== Given a vector space ''V'' over a field ''K'', the span of a set ''S'' of vectors (not necessarily finite) is defined to be the intersection ''W'' of all subspaces of ''V'' that contain ''S''. ''W'' is referred to as the subspace ''spanned by'' ''S'', or by the vectors in ''S''. Conversely, ''S'' is called a ''spanning set'' of ''W'', and we say that ''S'' ''spans'' ''W''. Alternatively, the span of ''S'' may be defined as the set of all finite linear combinations of elements of ''S'', which follows from the above definition. : In particular, if ''S'' is a finite subset of ''V'', then the span of ''S'' is the set of all linear combinations of the elements of ''S''. In the case of infinite ''S'', infinite linear combinations (i.e. where a combination may involve an infinite sum, assuming such sums are defined somehow, e.g. if ''V'' is a Banach space) are excluded by the definition; a generalization that allows these is not equivalent. 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「linear span」の詳細全文を読む スポンサード リンク
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