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In mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. Let denote the norm of vector ''x'' and the inner product of vectors ''x'' and ''y''. Then the underlying theorem, attributed to Fréchet, von Neumann and Jordan, is stated as:〔 〕〔 〕 :In a normed space (''V'', ), if the parallelogram law holds, then there is an inner product on ''V'' such that for all . ==Formula== The various forms given below are all related by the parallelogram law: : The polarization identity can be generalized to various other contexts in abstract algebra, linear algebra, and functional analysis. 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「polarization identity」の詳細全文を読む スポンサード リンク
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