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In mathematics, an asymmetric norm on a vector space is a generalization of the concept of a norm. ==Definition== Let ''X'' be a real vector space. Then an asymmetric norm on ''X'' is a function ''p'' : ''X'' → R satisfying the following properties: * non-negativity: for all ''x'' ∈ ''X'', ''p''(''x'') ≥ 0; * definiteness: for ''x'' ∈ ''X'', ''x'' = 0 if and only if ''p''(''x'') = ''p''(−''x'') = 0; * homogeneity: for all ''x'' ∈ ''X'' and all ''λ'' ≥ 0, ''p''(''λx'') = ''λp''(''x''); * the triangle inequality: for all ''x'', ''y'' ∈ ''X'', ''p''(''x'' + ''y'') ≤ ''p''(''x'') + ''p''(''y''). 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「asymmetric norm」の詳細全文を読む スポンサード リンク
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