"978"^^ . "Berlin, New York"@fr . . "In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W of a vector space V equipped with a bilinear form B is the set W\u22A5 of all vectors in V that are orthogonal to every vector in W. Informally, it is called the perp, short for perpendicular complement. It is a subspace of V."@en . . "Komplement\u00E4rraum"@de . . "Halmos"@fr . "Paul R."@fr . "In algebra lineare, il sottospazio ortogonale realizza il concetto di ortogonalit\u00E0 per sottospazi di uno spazio vettoriale munito di un prodotto scalare. Quando il prodotto scalare \u00E8 definito positivo, il sottospazio ortogonale \u00E8 spesso chiamato anche complemento ortogonale."@it . "Springer Verlag"@fr . . . "\u6570\u5B66\u306E\u7DDA\u578B\u4EE3\u6570\u5B66\u304A\u3088\u3073\u95A2\u6570\u89E3\u6790\u5B66\u306E\u5206\u91CE\u306B\u304A\u3044\u3066\u3001\u53CC\u7DDA\u578B\u5F62\u5F0F B \u3092\u5099\u3048\u308B\u30D9\u30AF\u30C8\u30EB\u7A7A\u9593 V \u306E\u3042\u308B\u90E8\u5206\u7A7A\u9593 W \u306E\u76F4\u4EA4\u88DC\u7A7A\u9593\uFF08\u3061\u3087\u3063\u3053\u3046\u307B\u304F\u3046\u304B\u3093\u3001\u82F1: orthogonal complement\uFF09\u3068\u306F\u3001W \u5185\u306E\u3059\u3079\u3066\u306E\u30D9\u30AF\u30C8\u30EB\u3068\u76F4\u4EA4\u3059\u308B\u3088\u3046\u306A V \u5185\u306E\u3059\u3079\u3066\u306E\u30D9\u30AF\u30C8\u30EB\u304B\u3089\u306A\u308B\u96C6\u5408 W\u22A5 \u306E\u3053\u3068\u3092\u8A00\u3046\u3002\u300Cperpendicular complement\u300D\u306E\u7565\u3068\u3057\u3066\u3001perp \u3068\u975E\u516C\u5F0F\u7684\u306B\u547C\u3070\u308C\u308B\u3053\u3068\u304C\u3042\u308B\u3002\u305D\u306E\u3088\u3046\u306A\u76F4\u4EA4\u88DC\u7A7A\u9593\u306F\u3001V \u306E\u90E8\u5206\u7A7A\u9593\u3067\u3042\u308B\u3002"@ja . "2124"^^ . . . . "Compl\u00E9ment orthogonal"@fr . . . "Dope\u0142nienie ortogonalne"@pl . "Orthogonal complement"@en . . "1478412"^^ . . "Springer"@fr . . "17"^^ . . . . "\u6570\u5B66\u306E\u7DDA\u578B\u4EE3\u6570\u5B66\u304A\u3088\u3073\u95A2\u6570\u89E3\u6790\u5B66\u306E\u5206\u91CE\u306B\u304A\u3044\u3066\u3001\u53CC\u7DDA\u578B\u5F62\u5F0F B \u3092\u5099\u3048\u308B\u30D9\u30AF\u30C8\u30EB\u7A7A\u9593 V \u306E\u3042\u308B\u90E8\u5206\u7A7A\u9593 W \u306E\u76F4\u4EA4\u88DC\u7A7A\u9593\uFF08\u3061\u3087\u3063\u3053\u3046\u307B\u304F\u3046\u304B\u3093\u3001\u82F1: orthogonal complement\uFF09\u3068\u306F\u3001W \u5185\u306E\u3059\u3079\u3066\u306E\u30D9\u30AF\u30C8\u30EB\u3068\u76F4\u4EA4\u3059\u308B\u3088\u3046\u306A V \u5185\u306E\u3059\u3079\u3066\u306E\u30D9\u30AF\u30C8\u30EB\u304B\u3089\u306A\u308B\u96C6\u5408 W\u22A5 \u306E\u3053\u3068\u3092\u8A00\u3046\u3002\u300Cperpendicular complement\u300D\u306E\u7565\u3068\u3057\u3066\u3001perp \u3068\u975E\u516C\u5F0F\u7684\u306B\u547C\u3070\u308C\u308B\u3053\u3068\u304C\u3042\u308B\u3002\u305D\u306E\u3088\u3046\u306A\u76F4\u4EA4\u88DC\u7A7A\u9593\u306F\u3001V \u306E\u90E8\u5206\u7A7A\u9593\u3067\u3042\u308B\u3002"@ja . . . "Ein Komplement oder ein komplement\u00E4rer Unterraum ist im mathematischen Teilgebiet der linearen Algebra ein m\u00F6glichst gro\u00DFer Unterraum, der einen vorgegebenen Unterraum nur im Nullpunkt schneidet. Der gesamte Vektorraum wird dadurch gewisserma\u00DFen in zwei unabh\u00E4ngige Teile zerlegt."@de . . . . . "110361337"^^ . . . . "Finite-dimensional vector spaces"@fr . "Ein Komplement oder ein komplement\u00E4rer Unterraum ist im mathematischen Teilgebiet der linearen Algebra ein m\u00F6glichst gro\u00DFer Unterraum, der einen vorgegebenen Unterraum nur im Nullpunkt schneidet. Der gesamte Vektorraum wird dadurch gewisserma\u00DFen in zwei unabh\u00E4ngige Teile zerlegt."@de . "1974"^^ . . . . "\u76F4\u4EA4\u88DC\u7A7A\u9593"@ja . . "In algebra lineare, il sottospazio ortogonale realizza il concetto di ortogonalit\u00E0 per sottospazi di uno spazio vettoriale munito di un prodotto scalare. Quando il prodotto scalare \u00E8 definito positivo, il sottospazio ortogonale \u00E8 spesso chiamato anche complemento ortogonale."@it . . . "Sottospazio ortogonale"@it . . . . "en"@fr . . . "Paul Halmos"@fr . . . . "\u041E\u0440\u0442\u043E\u0433\u043E\u043D\u0430\u043B\u044C\u043D\u043E\u0435 \u0434\u043E\u043F\u043E\u043B\u043D\u0435\u043D\u0438\u0435"@ru . . "In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W of a vector space V equipped with a bilinear form B is the set W\u22A5 of all vectors in V that are orthogonal to every vector in W. Informally, it is called the perp, short for perpendicular complement. It is a subspace of V."@en .