. . . . . . . "Transformaci\u00F3n de Householder"@es . . . . . . . . . . . . . "En matem\u00E1ticas, una transformaci\u00F3n de Householder es una transformaci\u00F3n lineal del espacio que consiste en una reflexi\u00F3n pura con respecto a un plano. Viene definida por una matriz de dimensi\u00F3n (N x N) tal que para cualquier vector de dimensi\u00F3n N se cumple que es la reflexi\u00F3n de respecto a un plano . La transformaci\u00F3n de Householder fue introducida por Alston Householder en 1958. Estas matrices (matrices de ) son ortogonales (sus vectores forman una base ortonormal) y son sim\u00E9tricas. Como consecuencia son iguales a su propia inversa."@es . "Trasformazione di Householder"@it . "En matem\u00E1ticas, una transformaci\u00F3n de Householder es una transformaci\u00F3n lineal del espacio que consiste en una reflexi\u00F3n pura con respecto a un plano. Viene definida por una matriz de dimensi\u00F3n (N x N) tal que para cualquier vector de dimensi\u00F3n N se cumple que es la reflexi\u00F3n de respecto a un plano . La transformaci\u00F3n de Householder fue introducida por Alston Householder en 1958. Estas matrices (matrices de ) son ortogonales (sus vectores forman una base ortonormal) y son sim\u00E9tricas. Como consecuencia son iguales a su propia inversa. Esta propiedad es f\u00E1cil de comprender si, acudiendo al sentido geom\u00E9trico de la transformaci\u00F3n, decimos que el reflejo del reflejo es el espacio original. El c\u00E1lculo de la matriz asociada a un plano de reflexi\u00F3n se hace a partir del vector normal al plano seg\u00FAn: Se puede comprobar que multiplicar un vector por la expresi\u00F3n anterior equivale a restarle el doble de su proyecci\u00F3n sobre el vector ; de donde resulta la reflexi\u00F3n."@es . . . . . "\u041F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430"@ru . "In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin. The Householder transformation was used in a 1958 paper by Alston Scott Householder. Its analogue over general inner product spaces is the Householder operator."@en . "Householder transformation"@en . "\u7DDA\u578B\u4EE3\u6570\u5B66\u306B\u304A\u3051\u308B\u30CF\u30A6\u30B9\u30DB\u30EB\u30C0\u30FC\u5909\u63DB\uFF08\u30CF\u30A6\u30B9\u30DB\u30EB\u30C0\u30FC\u3078\u3093\u304B\u3093\u3001\u82F1: Householder transformation\uFF09\u3001\u30CF\u30A6\u30B9\u30DB\u30EB\u30C0\u30FC\u93E1\u6620 (Householder reflection) \u3042\u308B\u3044\u306F\u57FA\u672C\u93E1\u6620\u5B50 (elementary reflector) \u306F\u3001\u539F\u70B9\u3092\u542B\u3080\u5E73\u9762\u307E\u305F\u306F\u8D85\u5E73\u9762\u306B\u95A2\u3059\u308B\u93E1\u6620\u3092\u8A18\u8FF0\u3059\u308B\u7DDA\u578B\u5909\u63DB\u3067\u3042\u308B\u3002\u30CF\u30A6\u30B9\u30DB\u30EB\u30C0\u30FC\u5909\u63DB\u306F \u304C\u5C0E\u5165\u3057\u305F\u3002\u4E00\u822C\u306E\u5185\u7A4D\u7A7A\u9593\u4E0A\u306B\u3082\u5BFE\u5FDC\u3059\u308B\u304C\u3042\u308B\u3002"@ja . . . "Transforma\u00E7\u00E3o de Householder"@pt . . . . "\u8C6A\u65AF\u970D\u5C14\u5FB7\u53D8\u6362"@zh . "In der Mathematik beschreibt die Householdertransformation die Spiegelung eines Vektors an einer Hyperebene durch Null im euklidischen Raum. Im dreidimensionalen Raum ist sie somit eine Spiegelung an einer Ebene (durch den Ursprung). Die Darstellung dieser linearen Abbildung durch eine Matrix wird als Householder-Matrix bezeichnet. Verwendung findet sie vor allem in der numerischen Mathematik, wenn mittels orthogonaler Transformationen Matrizen so gezielt umgeformt werden, dass bestimmte Spaltenvektoren auf das Vielfache des ersten Einheitsvektors abgebildet werden, insbesondere beim QR-Verfahren und der QR-Zerlegung."@de . . "\u041F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430"@uk . . "\u8C6A\u65AF\u970D\u5C14\u5FB7\u53D8\u6362\uFF08Householder transformation\uFF09\u6216\u8B6F\u300C\u8C6A\u65AF\u970D\u5FB7\u8F49\u63DB\u300D\uFF0C\u53C8\u79F0\u521D\u7B49\u53CD\u5C04\uFF08Elementary reflection\uFF09\uFF0C\u6700\u521D\u7531A.C Aitken\u57281932\u5E74\u63D0\u51FA\u3002\u57281958\u5E74\u6307\u51FA\u4E86\u8FD9\u4E00\u53D8\u6362\u5728\u6570\u503C\u7EBF\u6027\u4EE3\u6570\u4E0A\u7684\u610F\u4E49\u3002\u8FD9\u4E00\u53D8\u6362\u5C06\u4E00\u4E2A\u5411\u91CF\u53D8\u6362\u4E3A\u7531\u4E00\u4E2A\u8D85\u5E73\u9762\u53CD\u5C04\u7684\u955C\u50CF\uFF0C\u662F\u4E00\u79CD\u7EBF\u6027\u53D8\u6362\u3002\u5176\u53D8\u6362\u77E9\u9635\u88AB\u79F0\u4F5C\u8C6A\u65AF\u970D\u5C14\u5FB7\u77E9\u9635\uFF0C\u5728\u4E00\u822C\u5185\u79EF\u7A7A\u95F4\u4E2D\u7684\u7C7B\u6BD4\u88AB\u79F0\u4F5C\u3002\u8D85\u5E73\u9762\u7684\u6CD5\u5411\u91CF\u88AB\u79F0\u4F5C\u8C6A\u65AF\u970D\u5C14\u5FB7\u5411\u91CF\u3002"@zh . . . "Transformaci\u00F3 de Householder"@ca . . . "En Householdertransformation \u00E4r inom matematiken, specifikt linj\u00E4r algebra, en avbildning som i ett tredimensionellt vektorrum med skal\u00E4rprodukt reflekterar en vektor i ett plan (som inneh\u00E5ller origo, ett underrum). Detta kan generaliseras till alla \u00E4ndligtdimensionella vektorrum som reflektion av en vektor i ett som inneh\u00E5ller origo. Transformationen kan \u00E4ven generaliseras till allm\u00E4nna inre produktrum och kallas d\u00E5 . Transformen introducerades av 1958."@sv . "En Householdertransformation \u00E4r inom matematiken, specifikt linj\u00E4r algebra, en avbildning som i ett tredimensionellt vektorrum med skal\u00E4rprodukt reflekterar en vektor i ett plan (som inneh\u00E5ller origo, ett underrum). Detta kan generaliseras till alla \u00E4ndligtdimensionella vektorrum som reflektion av en vektor i ett som inneh\u00E5ller origo. Transformationen kan \u00E4ven generaliseras till allm\u00E4nna inre produktrum och kallas d\u00E5 . Transformen introducerades av 1958."@sv . "\u30CF\u30A6\u30B9\u30DB\u30EB\u30C0\u30FC\u5909\u63DB"@ja . "In der Mathematik beschreibt die Householdertransformation die Spiegelung eines Vektors an einer Hyperebene durch Null im euklidischen Raum. Im dreidimensionalen Raum ist sie somit eine Spiegelung an einer Ebene (durch den Ursprung). Die Darstellung dieser linearen Abbildung durch eine Matrix wird als Householder-Matrix bezeichnet. Verwendung findet sie vor allem in der numerischen Mathematik, wenn mittels orthogonaler Transformationen Matrizen so gezielt umgeformt werden, dass bestimmte Spaltenvektoren auf das Vielfache des ersten Einheitsvektors abgebildet werden, insbesondere beim QR-Verfahren und der QR-Zerlegung. Die Householdertransformation wurde 1958 durch den amerikanischen Mathematiker Alston Scott Householder eingef\u00FChrt."@de . . "Em \u00E1lgebra linear, uma transforma\u00E7\u00E3o de Householder (tamb\u00E9m conhecida como uma reflex\u00E3o de Householder ou refletor elementar) \u00E9 uma transforma\u00E7\u00E3o linear que descreve uma reflex\u00E3o em rela\u00E7\u00E3o a um plano ou hiperplano que cont\u00E9m a origem. A transforma\u00E7\u00E3o de Householder foi introduzida em 1958 por Alston Scott Householder. O seu an\u00E1logo em espa\u00E7os com produto interno mais gerais \u00E9 o operador de Householder."@pt . "\u8C6A\u65AF\u970D\u5C14\u5FB7\u53D8\u6362\uFF08Householder transformation\uFF09\u6216\u8B6F\u300C\u8C6A\u65AF\u970D\u5FB7\u8F49\u63DB\u300D\uFF0C\u53C8\u79F0\u521D\u7B49\u53CD\u5C04\uFF08Elementary reflection\uFF09\uFF0C\u6700\u521D\u7531A.C Aitken\u57281932\u5E74\u63D0\u51FA\u3002\u57281958\u5E74\u6307\u51FA\u4E86\u8FD9\u4E00\u53D8\u6362\u5728\u6570\u503C\u7EBF\u6027\u4EE3\u6570\u4E0A\u7684\u610F\u4E49\u3002\u8FD9\u4E00\u53D8\u6362\u5C06\u4E00\u4E2A\u5411\u91CF\u53D8\u6362\u4E3A\u7531\u4E00\u4E2A\u8D85\u5E73\u9762\u53CD\u5C04\u7684\u955C\u50CF\uFF0C\u662F\u4E00\u79CD\u7EBF\u6027\u53D8\u6362\u3002\u5176\u53D8\u6362\u77E9\u9635\u88AB\u79F0\u4F5C\u8C6A\u65AF\u970D\u5C14\u5FB7\u77E9\u9635\uFF0C\u5728\u4E00\u822C\u5185\u79EF\u7A7A\u95F4\u4E2D\u7684\u7C7B\u6BD4\u88AB\u79F0\u4F5C\u3002\u8D85\u5E73\u9762\u7684\u6CD5\u5411\u91CF\u88AB\u79F0\u4F5C\u8C6A\u65AF\u970D\u5C14\u5FB7\u5411\u91CF\u3002"@zh . "485424"^^ . . . . "13135"^^ . "In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin. The Householder transformation was used in a 1958 paper by Alston Scott Householder. Its analogue over general inner product spaces is the Householder operator."@en . . . . . "1108989564"^^ . . . "\uD558\uC6B0\uC2A4\uD640\uB354 \uBCC0\uD658(Householder reflection,Householder transformation)\uC740 \uC18C\uD589\uB82C\uC2DD\uC758 \uC7AC\uADC0\uC801\uC778 \uC808\uCC28\uC758 \uBC18\uBCF5 \uC218\uB834\uC73C\uB85C \uD558\uC6B0\uC2A4\uD640\uB354 \uB9AC\uD50C\uB809\uD130(Householder reflector)\uB97C \uAD6C\uC131\uD55C\uB2E4. QR \uBD84\uD574\uC5D0\uC11C \uD558\uC6B0\uC2A4\uD640\uB354 \uB9AC\uD50C\uB809\uD130\uB97C \uC774\uC6A9\uD558\uC5EC \uD55C \uC5F4\uC529\uC744 \uC0C1\uC0BC\uAC01\uD589\uB82C\uB85C \uC811\uADFC\uD574 \uBC14\uAFB8\uC5B4\uAC10\uC73C\uB85C\uC368 \uC640 \uC744 \uAD6C\uD560 \uC218 \uC788\uB294\uB370, \uC774 \uBC29\uBC95\uC740 \uD589\uB82C\uC744 \uD558\uC6B0\uC2A4\uD640\uB354 \uD589\uB82C\uC758 \uACF1\uC73C\uB85C \uAD6C\uD574\uC8FC\uAE30 \uB54C\uBB38\uC5D0, \uC9C1\uC811 \uB97C \uAD6C\uD560 \uC218 \uC5C6\uC744 \uB54C \uC720\uC6A9\uD558\uB2E4. \uB610\uD55C \uBD80\uB3D9\uC18C\uC218\uC810 \uC5F0\uC0B0\uC5D0\uC11C\uB3C4 \uC624\uCC28\uAC00 \uB204\uC801\uB418\uC9C0 \uC54A\uB294 \uC131\uC9C8\uC774 \uC788\uB2E4. \uB610, \uADF8\uB78C-\uC288\uBBF8\uD2B8 \uBC29\uBC95\uACFC \uAE30\uBE10\uC2A4 \uD68C\uC804 \uBC29\uBC95\uACFC \uD568\uAED8 QR \uBD84\uD574\uC5D0\uC11C \uACE0\uC720\uD55C \uBC29\uBC95\uC744 \uC81C\uACF5\uD55C\uB2E4. \uD558\uC6B0\uC2A4\uD640\uB354 \uBCC0\uD658\uC740 \uBC34\uB4DC \uD589\uB82C\uC758 \uC77C\uC885\uC778 3\uC911\uB300\uAC01\uD589\uB82C\uCC98\uB7FC \uBC34\uB4DC \uD589\uB82C\uC744 \uB9CC\uB4E4\uAE30\uB3C4 \uD55C\uB2E4."@ko . . . . "In matematica, una trasformazione di Householder in uno spazio tridimensionale \u00E8 la riflessione dei vettori rispetto ad un piano passante per l'origine. In generale in uno spazio euclideo essa \u00E8 una trasformazione lineare che descrive una riflessione rispetto ad un iperpiano contenente l'origine. La trasformazione di Householder \u00E8 stata introdotta nel 1958 dal matematico statunitense Alston Scott Householder (1905-1993). Questa pu\u00F2 essere usata per ottenere una fattorizzazione QR di una matrice."@it . . . "En el camp matem\u00E0tic de l'\u00E0lgebra lineal, una transformaci\u00F3 de Householder (tamb\u00E9 coneguda com a reflexi\u00F3 de Householder) \u00E9s una transformaci\u00F3 lineal que descriu una reflexi\u00F3 respecte a un pla o hiperpl\u00E0 que cont\u00E9 l'origen. Les transformacions de Householder s'usen \u00E0mpliament en \u00E0lgebra lineal num\u00E8rica, com a eina per realitzar descomposicions QR i en el primer pas de l'. La transformaci\u00F3 de Householder fou introdu\u00EFda l'any 1958 per Alston Scott Householder. El concepte an\u00E0leg sobre espais prehilbertians generals \u00E9s l'."@ca . . . . . "Householdertransformatie"@nl . . "\uD558\uC6B0\uC2A4\uD640\uB354 \uBCC0\uD658"@ko . . . "\u041F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430 (\u043E\u043F\u0435\u0440\u0430\u0442\u043E\u0440 \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430) \u2014 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430 , \u043A\u043E\u0442\u043E\u0440\u043E\u0435 \u043E\u043F\u0438\u0441\u044B\u0432\u0430\u0435\u0442 \u0435\u0433\u043E \u043E\u0442\u0440\u0430\u0436\u0435\u043D\u0438\u0435 \u043E\u0442\u043D\u043E\u0441\u0438\u0442\u0435\u043B\u044C\u043D\u043E \u0433\u0438\u043F\u0435\u0440\u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u0438, \u043F\u0440\u043E\u0445\u043E\u0434\u044F\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u043D\u0430\u0447\u0430\u043B\u043E \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442. \u0418\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u043B\u043E\u0441\u044C \u0432 \u0440\u0430\u0431\u043E\u0442\u0435 \u0430\u043C\u0435\u0440\u0438\u043A\u0430\u043D\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u042D\u043B\u0441\u0442\u043E\u043D\u0430 \u0421\u043A\u043E\u0442\u0442\u0430 \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430 1958 \u0433\u043E\u0434\u0430. \u0428\u0438\u0440\u043E\u043A\u043E \u043F\u0440\u0438\u043C\u0435\u043D\u044F\u0435\u0442\u0441\u044F \u0432 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0435 \u0434\u043B\u044F QR-\u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u043C\u0430\u0442\u0440\u0438\u0446\u044B."@ru . "In de lineaire algebra is een householdertransformatie een reflectie (spiegeling) in de euclidische ruimte ten opzichte van een hypervlak dat door de oorsprong gaat. Het spiegelvlak wordt bepaald door een normaalvector u van lengte 1 (een eenheidsvector). De transformatie is een voorbeeld van een lineaire afbeelding. De transformatie is genoemd naar de Amerikaanse wiskundige , die ze in 1958 invoerde. In matrixvorm kan ze uitgedrukt worden als: , waarin de eenheidsmatrix is. De matrix is symmetrisch en orthogonaal. Het product van met een vector komt overeen met de spiegeling van aan het hypervlak door de oorsprong loodrecht op ."@nl . "In de lineaire algebra is een householdertransformatie een reflectie (spiegeling) in de euclidische ruimte ten opzichte van een hypervlak dat door de oorsprong gaat. Het spiegelvlak wordt bepaald door een normaalvector u van lengte 1 (een eenheidsvector). De transformatie is een voorbeeld van een lineaire afbeelding. De transformatie is genoemd naar de Amerikaanse wiskundige , die ze in 1958 invoerde. In matrixvorm kan ze uitgedrukt worden als: ,"@nl . "\uD558\uC6B0\uC2A4\uD640\uB354 \uBCC0\uD658(Householder reflection,Householder transformation)\uC740 \uC18C\uD589\uB82C\uC2DD\uC758 \uC7AC\uADC0\uC801\uC778 \uC808\uCC28\uC758 \uBC18\uBCF5 \uC218\uB834\uC73C\uB85C \uD558\uC6B0\uC2A4\uD640\uB354 \uB9AC\uD50C\uB809\uD130(Householder reflector)\uB97C \uAD6C\uC131\uD55C\uB2E4. QR \uBD84\uD574\uC5D0\uC11C \uD558\uC6B0\uC2A4\uD640\uB354 \uB9AC\uD50C\uB809\uD130\uB97C \uC774\uC6A9\uD558\uC5EC \uD55C \uC5F4\uC529\uC744 \uC0C1\uC0BC\uAC01\uD589\uB82C\uB85C \uC811\uADFC\uD574 \uBC14\uAFB8\uC5B4\uAC10\uC73C\uB85C\uC368 \uC640 \uC744 \uAD6C\uD560 \uC218 \uC788\uB294\uB370, \uC774 \uBC29\uBC95\uC740 \uD589\uB82C\uC744 \uD558\uC6B0\uC2A4\uD640\uB354 \uD589\uB82C\uC758 \uACF1\uC73C\uB85C \uAD6C\uD574\uC8FC\uAE30 \uB54C\uBB38\uC5D0, \uC9C1\uC811 \uB97C \uAD6C\uD560 \uC218 \uC5C6\uC744 \uB54C \uC720\uC6A9\uD558\uB2E4. \uB610\uD55C \uBD80\uB3D9\uC18C\uC218\uC810 \uC5F0\uC0B0\uC5D0\uC11C\uB3C4 \uC624\uCC28\uAC00 \uB204\uC801\uB418\uC9C0 \uC54A\uB294 \uC131\uC9C8\uC774 \uC788\uB2E4. \uB610, \uADF8\uB78C-\uC288\uBBF8\uD2B8 \uBC29\uBC95\uACFC \uAE30\uBE10\uC2A4 \uD68C\uC804 \uBC29\uBC95\uACFC \uD568\uAED8 QR \uBD84\uD574\uC5D0\uC11C \uACE0\uC720\uD55C \uBC29\uBC95\uC744 \uC81C\uACF5\uD55C\uB2E4. \uD558\uC6B0\uC2A4\uD640\uB354 \uBCC0\uD658\uC740 \uBC34\uB4DC \uD589\uB82C\uC758 \uC77C\uC885\uC778 3\uC911\uB300\uAC01\uD589\uB82C\uCC98\uB7FC \uBC34\uB4DC \uD589\uB82C\uC744 \uB9CC\uB4E4\uAE30\uB3C4 \uD55C\uB2E4."@ko . . . . . "Em \u00E1lgebra linear, uma transforma\u00E7\u00E3o de Householder (tamb\u00E9m conhecida como uma reflex\u00E3o de Householder ou refletor elementar) \u00E9 uma transforma\u00E7\u00E3o linear que descreve uma reflex\u00E3o em rela\u00E7\u00E3o a um plano ou hiperplano que cont\u00E9m a origem. A transforma\u00E7\u00E3o de Householder foi introduzida em 1958 por Alston Scott Householder. O seu an\u00E1logo em espa\u00E7os com produto interno mais gerais \u00E9 o operador de Householder."@pt . "\u041F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430 (\u043E\u043F\u0435\u0440\u0430\u0442\u043E\u0440 \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430) \u2014 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0435 \u043F\u0440\u0435\u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u0435 \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430 , \u043A\u043E\u0442\u043E\u0440\u043E\u0435 \u043E\u043F\u0438\u0441\u044B\u0432\u0430\u0435\u0442 \u0435\u0433\u043E \u043E\u0442\u0440\u0430\u0436\u0435\u043D\u0438\u0435 \u043E\u0442\u043D\u043E\u0441\u0438\u0442\u0435\u043B\u044C\u043D\u043E \u0433\u0438\u043F\u0435\u0440\u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u0438, \u043F\u0440\u043E\u0445\u043E\u0434\u044F\u0449\u0435\u0439 \u0447\u0435\u0440\u0435\u0437 \u043D\u0430\u0447\u0430\u043B\u043E \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442. \u0418\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u043B\u043E\u0441\u044C \u0432 \u0440\u0430\u0431\u043E\u0442\u0435 \u0430\u043C\u0435\u0440\u0438\u043A\u0430\u043D\u0441\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u042D\u043B\u0441\u0442\u043E\u043D\u0430 \u0421\u043A\u043E\u0442\u0442\u0430 \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430 1958 \u0433\u043E\u0434\u0430. \u0428\u0438\u0440\u043E\u043A\u043E \u043F\u0440\u0438\u043C\u0435\u043D\u044F\u0435\u0442\u0441\u044F \u0432 \u043B\u0438\u043D\u0435\u0439\u043D\u043E\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0435 \u0434\u043B\u044F QR-\u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u043C\u0430\u0442\u0440\u0438\u0446\u044B."@ru . . . "Householdertransformation"@sv . "Householdertransformation"@de . "\u7DDA\u578B\u4EE3\u6570\u5B66\u306B\u304A\u3051\u308B\u30CF\u30A6\u30B9\u30DB\u30EB\u30C0\u30FC\u5909\u63DB\uFF08\u30CF\u30A6\u30B9\u30DB\u30EB\u30C0\u30FC\u3078\u3093\u304B\u3093\u3001\u82F1: Householder transformation\uFF09\u3001\u30CF\u30A6\u30B9\u30DB\u30EB\u30C0\u30FC\u93E1\u6620 (Householder reflection) \u3042\u308B\u3044\u306F\u57FA\u672C\u93E1\u6620\u5B50 (elementary reflector) \u306F\u3001\u539F\u70B9\u3092\u542B\u3080\u5E73\u9762\u307E\u305F\u306F\u8D85\u5E73\u9762\u306B\u95A2\u3059\u308B\u93E1\u6620\u3092\u8A18\u8FF0\u3059\u308B\u7DDA\u578B\u5909\u63DB\u3067\u3042\u308B\u3002\u30CF\u30A6\u30B9\u30DB\u30EB\u30C0\u30FC\u5909\u63DB\u306F \u304C\u5C0E\u5165\u3057\u305F\u3002\u4E00\u822C\u306E\u5185\u7A4D\u7A7A\u9593\u4E0A\u306B\u3082\u5BFE\u5FDC\u3059\u308B\u304C\u3042\u308B\u3002"@ja . . "\u041F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430 (\u043E\u043F\u0435\u0440\u0430\u0442\u043E\u0440 \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430) \u2014 \u043B\u0456\u043D\u0456\u0439\u043D\u0435 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0443 , \u0449\u043E \u043E\u043F\u0438\u0441\u0443\u0454 \u0439\u043E\u0433\u043E \u0432\u0456\u0434\u0434\u0437\u0435\u0440\u043A\u0430\u043B\u0435\u043D\u043D\u044F (\u0441\u0438\u043C\u0435\u0442\u0440\u0456\u044E) \u0449\u043E\u0434\u043E \u0433\u0456\u043F\u0435\u0440\u043F\u043B\u043E\u0449\u0438\u043D\u0438, \u044F\u043A\u0430 \u043F\u0440\u043E\u0445\u043E\u0434\u0438\u0442\u044C \u0447\u0435\u0440\u0435\u0437 \u043F\u043E\u0447\u0430\u0442\u043E\u043A \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442. \u0411\u0443\u043B\u043E \u0437\u0430\u043F\u0440\u043E\u043F\u043E\u043D\u043E\u0432\u0430\u043D\u0435 \u0432 1958 \u0430\u043C\u0435\u0440\u0438\u043A\u0430\u043D\u0441\u044C\u043A\u0438\u043C \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u043E\u043C \u0415\u043B\u0441\u0442\u043E\u043D\u043E\u043C \u0421\u043A\u043E\u0442\u043E\u043C \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u043E\u043C. \u0417\u0430\u0441\u0442\u043E\u0441\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0432 \u043B\u0456\u043D\u0456\u0439\u043D\u0456\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0456 \u0434\u043B\u044F QR-\u0440\u043E\u0437\u043A\u043B\u0430\u0434\u0443 \u043C\u0430\u0442\u0440\u0438\u0446\u0456."@uk . . . . . . . "En el camp matem\u00E0tic de l'\u00E0lgebra lineal, una transformaci\u00F3 de Householder (tamb\u00E9 coneguda com a reflexi\u00F3 de Householder) \u00E9s una transformaci\u00F3 lineal que descriu una reflexi\u00F3 respecte a un pla o hiperpl\u00E0 que cont\u00E9 l'origen. Les transformacions de Householder s'usen \u00E0mpliament en \u00E0lgebra lineal num\u00E8rica, com a eina per realitzar descomposicions QR i en el primer pas de l'. La transformaci\u00F3 de Householder fou introdu\u00EFda l'any 1958 per Alston Scott Householder. El concepte an\u00E0leg sobre espais prehilbertians generals \u00E9s l'."@ca . . . . . "In matematica, una trasformazione di Householder in uno spazio tridimensionale \u00E8 la riflessione dei vettori rispetto ad un piano passante per l'origine. In generale in uno spazio euclideo essa \u00E8 una trasformazione lineare che descrive una riflessione rispetto ad un iperpiano contenente l'origine. La trasformazione di Householder \u00E8 stata introdotta nel 1958 dal matematico statunitense Alston Scott Householder (1905-1993). Questa pu\u00F2 essere usata per ottenere una fattorizzazione QR di una matrice."@it . . . . . "\u041F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430 (\u043E\u043F\u0435\u0440\u0430\u0442\u043E\u0440 \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u0430) \u2014 \u043B\u0456\u043D\u0456\u0439\u043D\u0435 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0443 , \u0449\u043E \u043E\u043F\u0438\u0441\u0443\u0454 \u0439\u043E\u0433\u043E \u0432\u0456\u0434\u0434\u0437\u0435\u0440\u043A\u0430\u043B\u0435\u043D\u043D\u044F (\u0441\u0438\u043C\u0435\u0442\u0440\u0456\u044E) \u0449\u043E\u0434\u043E \u0433\u0456\u043F\u0435\u0440\u043F\u043B\u043E\u0449\u0438\u043D\u0438, \u044F\u043A\u0430 \u043F\u0440\u043E\u0445\u043E\u0434\u0438\u0442\u044C \u0447\u0435\u0440\u0435\u0437 \u043F\u043E\u0447\u0430\u0442\u043E\u043A \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442. \u0411\u0443\u043B\u043E \u0437\u0430\u043F\u0440\u043E\u043F\u043E\u043D\u043E\u0432\u0430\u043D\u0435 \u0432 1958 \u0430\u043C\u0435\u0440\u0438\u043A\u0430\u043D\u0441\u044C\u043A\u0438\u043C \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u043E\u043C \u0415\u043B\u0441\u0442\u043E\u043D\u043E\u043C \u0421\u043A\u043E\u0442\u043E\u043C \u0425\u0430\u0443\u0441\u0445\u043E\u043B\u0434\u0435\u0440\u043E\u043C. \u0417\u0430\u0441\u0442\u043E\u0441\u043E\u0432\u0443\u0454\u0442\u044C\u0441\u044F \u0432 \u043B\u0456\u043D\u0456\u0439\u043D\u0456\u0439 \u0430\u043B\u0433\u0435\u0431\u0440\u0456 \u0434\u043B\u044F QR-\u0440\u043E\u0437\u043A\u043B\u0430\u0434\u0443 \u043C\u0430\u0442\u0440\u0438\u0446\u0456."@uk . . "Transformation de Householder"@fr . .