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In mathematics, Auerbach's lemma, named after Herman Auerbach, is a theorem in functional analysis which asserts that a certain property of Euclidean spaces holds for general finite-dimensional normed vector spaces. == Statement == Let (''V'', ||·||) be an ''n''-dimensional normed vector space. Then there exists a basis of V such that : ||''e''''i''|| = 1 and ||''e''''i''|| = 1 for ''i'' = 1, ..., ''n'' where is a basis of ''V'' * dual to , i. e. ''e''''i''(''e''''j'') = δ''ij''. A basis with this property is called an ''Auerbach basis''. If ''V'' is a Euclidean space (or even infinite-dimensional Hilbert space) then this result is obvious as one may take for any orthonormal basis of ''V'' (the dual basis is then ). 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「Auerbach's lemma」の詳細全文を読む スポンサード リンク
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