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

IEV ref102-03-04

en
vector, <mathematics>
element of a vector space

Note 1 to entry: An n-dimensional vector is represented by an ordered set of n scalars, usually real or complex numbers, which depend on the choice of the base. In matrix notation, these scalars are usually represented as a column matrix:
U=( U 1 U 2 U n ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfacqGH9aqpda qadaqaauaabeqGeeaaaaqaaiaadwfadaWgaaqaaKqzGeGaaGymaaGc beaaaeaacaWGvbWaaSbaaeaajugibiaaikdaaOqabaaabaGaeSO7I0 eabaGaamyvamaaBaaabaGaamOBaaqabaaaaaGaayjkaiaawMcaaaaa @4546@

Note 2 to entry: A vector in a Euclidean space is characterized by its magnitude and, if it is a non-zero vector, by its direction.

Note 3 to entry: A complex vector U is defined by a real part and an imaginary part:
U=A+jB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaaCyvaiabg2 da9iaahgeacqGHRaWkcaGGQbGaaCOqaaaa@3EC5@ where A and B are real vectors.

Note 4 to entry: A vector is indicated by a letter symbol in sloped boldface type or by an arrow above a sloped lightface letter symbol: U or U MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaa4WaaCbiaKqzafqaai aadwfaaeqaleaacWaGKAOKH4kaaaaa@3DC6@ . The vector U with components U i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadwfadaWgaaWcba qcLboacaWGPbaaleqaaaaa@3C1A@ can be denoted ( U i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaaiikaiaadw fakmaaBaaaleaajug4aiaadMgaaSqabaGccaGGPaaaaa@3E36@ .

Note 5 to entry: The term "vector" is also used for a vector quantity.

Note 6 to entry: In geometry, the term “vector” is often used for a directed line segment in a point space.


fr
vecteur, <mathématiques> m
élément d'un espace vectoriel

Note 1 à l'article: Un vecteur à n dimensions est représenté par un ensemble ordonné de n scalaires, généralement des nombres réels ou complexes, qui dépendent du choix de la base. En notation matricielle, ces scalaires sont généralement représentés par une matrice-colonne:
U=( U 1 U 2 U n ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfacqGH9aqpda qadaqaauaabeqGeeaaaaqaaiaadwfadaWgaaqaaKqzGeGaaGymaaGc beaaaeaacaWGvbWaaSbaaeaajugibiaaikdaaOqabaaabaGaeSO7I0 eabaGaamyvamaaBaaabaGaamOBaaqabaaaaaGaayjkaiaawMcaaaaa @4546@

Note 2 à l'article: Un vecteur dans un espace euclidien est caractérisé par sa norme et, s'il n'est pas nul, par sa direction.

Note 3 à l'article: Un vecteur complexe U est défini par une partie réelle et une partie imaginaire: U=A+jB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaaCyvaiabg2 da9iaahgeacqGHRaWkcaGGQbGaaCOqaaaa@3EC5@ A et B sont des vecteurs réels.

Note 4 à l'article: Un vecteur est représenté par un symbole littéral en gras et en italique ou par un symbole en maigre et en italique surmonté d'une flèche: U ou U MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaa4WaaCbiaKqzafqaai aadwfaaeqaleaacWaGKAOKH4kaaaaa@3DC6@ . Le vecteur U de coordonnées U i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadwfadaWgaaWcba qcLboacaWGPbaaleqaaaaa@3C1A@ peut être représenté par ( U i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaaiikaiaadw fakmaaBaaaleaajug4aiaadMgaaSqabaGccaGGPaaaaa@3E36@ .

Note 5 à l'article: Le terme «vecteur» est aussi employé pour une grandeur vectorielle.

Note 6 à l’article: En géométrie, le terme «vecteur» est souvent employé pour désigner un segment de droite orienté dans un espace affine.


de
Vektor (1), m

es
vector (1)

ja
ベクトル, 関連エントリー102-03-21

pl
wektor (1)

pt
vector

sr
вектор, м јд

sv
vektor

zh
向量, <相关条目:102-03-21>

Publication date: 2017-07
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