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Area Mathematics - General concepts and linear algebra / Vectors and tensors

IEV ref102-03-22

en
component, <of a vector quantity>
coordinate, <of a vector quantity>
any of the n scalar quantities Q 1 , Q 2 , , Q n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgfadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaadgfadaWgaaWcbaGaaGOmaaqa baGccaqGSaGaaeiiaiablAciljaabYcacaqGGaGaamyuamaaBaaale aacaWGUbaabeaaaaa@4369@ in the representation of a vector quantity Q as the linear combination Q 1 a 1 + Q 2 a 2 ++ Q n a n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgfadaWgaaWcba GaaGymaaqabaGccaWHHbWaaSbaaSqaaiaaigdaaeqaaOGaey4kaSIa amyuamaaBaaaleaacaaIYaaabeaakiaahggadaWgaaWcbaGaaGOmaa qabaGccqGHRaWkcqWIMaYscqGHRaWkcaWGrbWaaSbaaSqaaiaad6ga aeqaaOGaaCyyamaaBaaaleaacaWGUbaabeaaaaa@47E3@ of the base vectors a 1 , a 2 , , a n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahggadaWgaaWcba qcLbqacaaIXaaaleqaaOGaaeilaiaabccacaWHHbWaaSbaaSqaaKqz aeGaaGOmaaWcbeaakiaabYcacaqGGaGaeSOjGSKaaeilaiaabccaca WHHbWaaSbaaSqaaiaad6gaaeqaaaaa@4499@

Note 1 to entry: Instead of treating each component of a vector quantity as a quantity (i.e. the product of a numerical value and a unit of measurement), the vector quantity Q may be represented as a vector of numerical values multiplied by the unit:
Q={ Q 1 }[Q] e 1 +{ Q 2 }[Q] e 2 +{ Q 3 }[Q] e 3 =( { Q 1 } e 1 +{ Q 2 } e 2 +{ Q 3 } e 3 )[Q] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahgfacqGH9aqpda GadaqaaiaadgfadaWgaaWcbaGaaGymaaqabaaakiaawUhacaGL9baa caaMc8+aamWaaeaacaWGrbaacaGLBbGaayzxaaGaaGPaVlaahwgada WgaaWcbaGaaGymaaqabaGccqGHRaWkdaGadaqaaiaadgfadaWgaaWc baGaaGOmaaqabaaakiaawUhacaGL9baacaaMc8+aamWaaeaacaWGrb aacaGLBbGaayzxaaGaaGPaVlaahwgadaWgaaWcbaGaaGOmaaqabaGc cqGHRaWkdaGadaqaaiaadgfadaWgaaWcbaGaaG4maaqabaaakiaawU hacaGL9baacaaMc8+aamWaaeaacaWGrbaacaGLBbGaayzxaaGaaGPa VlaahwgadaWgaaWcbaGaaG4maaqabaGccqGH9aqpdaqadaqaamaacm aabaGaamyuamaaBaaaleaacaaIXaaabeaaaOGaay5Eaiaaw2haaiaa ykW7caWHLbWaaSbaaSqaaiaaigdaaeqaaOGaey4kaSYaaiWaaeaaca WGrbWaaSbaaSqaaiaaikdaaeqaaaGccaGL7bGaayzFaaGaaGPaVlaa hwgadaWgaaWcbaGaaGOmaaqabaGccqGHRaWkdaGadaqaaiaadgfada WgaaWcbaGaaG4maaqabaaakiaawUhacaGL9baacaaMc8UaaCyzamaa BaaaleaacaaIZaaabeaaaOGaayjkaiaawMcaaiaaykW7daWadaqaai aadgfaaiaawUfacaGLDbaaaaa@7E68@
where { Q 1 },{ Q 2 },{ Q 3 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaacmaabaGaamyuam aaBaaaleaacaaIXaaabeaaaOGaay5Eaiaaw2haaiaacYcacaaMe8+a aiWaaeaacaWGrbWaaSbaaSqaaiaaikdaaeqaaaGccaGL7bGaayzFaa GaaiilaiaaysW7daGadaqaaiaadgfadaWgaaWcbaGaaG4maaqabaaa kiaawUhacaGL9baaaaa@4932@ are numerical values, [Q] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaadmaabaGaamyuaa Gaay5waiaaw2faaaaa@3B95@ is the unit, and e 1 , e 2 , e 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwgadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaahwgadaWgaaWcbaGaaGOmaaqa baGccaqGSaGaaeiiaiaahwgadaWgaaWcbaGaaG4maaqabaGccaqGGa aaaa@41B4@ are the unit vectors. Similar considerations apply to tensor quantities.

Note 2 to entry: The components of a vector quantity are transformed by a coordinate transformation like the coordinates of a position vector.

Note 3 to entry: The term "coordinate" is generally used when the vector quantity is a position vector. This usage is consistent with the definition of the coordinates of a vector in mathematics (IEV 102-03-09).


fr
composante, <d'une grandeur vectorielle> f
chacune des n grandeurs scalaires Q 1 , Q 2 , , Q n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgfadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaadgfadaWgaaWcbaGaaGOmaaqa baGccaqGSaGaaeiiaiablAciljaabYcacaqGGaGaamyuamaaBaaale aacaWGUbaabeaaaaa@4369@ dans la représentation d'une grandeur vectorielle Q comme la combinaison linéaire Q 1 a 1 + Q 2 a 2 ++ Q n a n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgfadaWgaaWcba GaaGymaaqabaGccaWHHbWaaSbaaSqaaiaaigdaaeqaaOGaey4kaSIa amyuamaaBaaaleaacaaIYaaabeaakiaahggadaWgaaWcbaGaaGOmaa qabaGccqGHRaWkcqWIMaYscqGHRaWkcaWGrbWaaSbaaSqaaiaad6ga aeqaaOGaaCyyamaaBaaaleaacaWGUbaabeaaaaa@47E3@ des vecteurs de base a 1 , a 2 , , a n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahggadaWgaaWcba qcLbqacaaIXaaaleqaaOGaaeilaiaabccacaWHHbWaaSbaaSqaaKqz aeGaaGOmaaWcbeaakiaabYcacaqGGaGaeSOjGSKaaeilaiaabccaca WHHbWaaSbaaSqaaiaad6gaaeqaaaaa@4499@

Note 1 à l'article: Au lieu de traiter chaque coordonnée comme une grandeur (c'est-à-dire la produit de sa valeur numérique par l'unité de mesure), on peut exprimer la grandeur vectorielle Q comme le produit d'un vecteur de valeurs numériques par l'unité:

Q={ Q 1 }[Q] e 1 +{ Q 2 }[Q] e 2 +{ Q 3 }[Q] e 3 =( { Q 1 } e 1 +{ Q 2 } e 2 +{ Q 3 } e 3 )[Q] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahgfacqGH9aqpda GadaqaaiaadgfadaWgaaWcbaGaaGymaaqabaaakiaawUhacaGL9baa caaMc8+aamWaaeaacaWGrbaacaGLBbGaayzxaaGaaGPaVlaahwgada WgaaWcbaGaaGymaaqabaGccqGHRaWkdaGadaqaaiaadgfadaWgaaWc baGaaGOmaaqabaaakiaawUhacaGL9baacaaMc8+aamWaaeaacaWGrb aacaGLBbGaayzxaaGaaGPaVlaahwgadaWgaaWcbaGaaGOmaaqabaGc cqGHRaWkdaGadaqaaiaadgfadaWgaaWcbaGaaG4maaqabaaakiaawU hacaGL9baacaaMc8+aamWaaeaacaWGrbaacaGLBbGaayzxaaGaaGPa VlaahwgadaWgaaWcbaGaaG4maaqabaGccqGH9aqpdaqadaqaamaacm aabaGaamyuamaaBaaaleaacaaIXaaabeaaaOGaay5Eaiaaw2haaiaa ykW7caWHLbWaaSbaaSqaaiaaigdaaeqaaOGaey4kaSYaaiWaaeaaca WGrbWaaSbaaSqaaiaaikdaaeqaaaGccaGL7bGaayzFaaGaaGPaVlaa hwgadaWgaaWcbaGaaGOmaaqabaGccqGHRaWkdaGadaqaaiaadgfada WgaaWcbaGaaG4maaqabaaakiaawUhacaGL9baacaaMc8UaaCyzamaa BaaaleaacaaIZaaabeaaaOGaayjkaiaawMcaaiaaykW7daWadaqaai aadgfaaiaawUfacaGLDbaaaaa@7E68@

{ Q 1 },{ Q 2 },{ Q 3 } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaacmaabaGaamyuam aaBaaaleaacaaIXaaabeaaaOGaay5Eaiaaw2haaiaacYcacaaMe8+a aiWaaeaacaWGrbWaaSbaaSqaaiaaikdaaeqaaaGccaGL7bGaayzFaa GaaiilaiaaysW7daGadaqaaiaadgfadaWgaaWcbaGaaG4maaqabaaa kiaawUhacaGL9baaaaa@4932@ sont des valeurs numériques, [Q] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaadmaabaGaamyuaa Gaay5waiaaw2faaaaa@3B95@ est l'unité et e 1 , e 2 , e 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwgadaWgaaWcba GaaGymaaqabaGccaqGSaGaaeiiaiaahwgadaWgaaWcbaGaaGOmaaqa baGccaqGSaGaaeiiaiaahwgadaWgaaWcbaGaaG4maaqabaGccaqGGa aaaa@41B4@ sont les vecteurs unitaires. Les grandeurs tensorielles peuvent être traitées de manière analogue.

Note 2 à l'article: Les composantes d'une grandeur vectorielle sont transformées par un changement de coordonnées de la même manière que les coordonnées d'un rayon vecteur.

Note 3 à l'article: Le terme «coordonnée» est généralement employé lorsque la grandeur vectorielle est un rayon vecteur. Cet usage est compatible avec la définition des coordonnées d'un vecteur en mathématiques (IEV 102-03-09).


de
Komponente (einer Vektorgröße), f

es
componente (de una magnitud vectorial)

ja
成分, <ベクトル座標の>
座標, <ベクトル量の>

pl
współrzędna (wielkości wektorowej)

pt
componente (de uma grandeza vectorial)

sr
компонента, <векторске величине> ж јд
координата, <векторске величине> ж јд

sv
komponent (av en vektorstorhet)

zh
分量, <向量量的>
坐标, <向量量的>

Publication date: 2008-08
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