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

IEV ref102-03-46

en
tensor product, <of a tensor and a vector>
tensor of the third order defined by the trilinear form equal to the product of the bilinear form defining a tensor of the second order on a given Euclidean space and the linear form identified with a vector in the same space

Note 1 to entry: The components of the tensor product of the tensor T and the vector U are: (TU) ijk = T ij U k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaaiikaGqadi aa=rfacqGHxkcXcaWHvbGaaiykaOWaaSbaaSqaaiaadMgacaWGQbGa am4AaaqabaGccqGH9aqpjugqbiaadsfakmaaBaaaleaacaWGPbGaam OAaaqabaqcLbuacaWGvbGcdaWgaaWcbaGaam4Aaaqabaaaaa@457C@ .

Note 2 to entry: The tensor product of a tensor and a vector is denoted by TU MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadKqzafGaa8hvai abgEPielaa=nfaaaa@39BC@ .


fr
produit tensoriel, <d'un tenseur et d'un vecteur> m
tenseur du troisième ordre défini par la forme trilinéaire égale au produit de la forme bilinéaire qui définit un tenseur du deuxième ordre sur un espace euclidien donné et de la forme linéaire identifiée à un vecteur du même espace

Note 1 à l'article: Les coordonnées du produit tensoriel d'un tenseur T et d'un vecteur U sont: (TU) ijk = T ij U k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaaiikaGqadi aa=rfacqGHxkcXcaWHvbGaaiykaOWaaSbaaSqaaiaadMgacaWGQbGa am4AaaqabaGccqGH9aqpjugqbiaadsfakmaaBaaaleaacaWGPbGaam OAaaqabaqcLbuacaWGvbGcdaWgaaWcbaGaam4Aaaqabaaaaa@457C@ .

Note 2 à l'article: Le produit tensoriel d'un tenseur et d'un vecteur est noté TU MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadKqzafGaa8hvai abgEPielaa=nfaaaa@39BC@ .


de
Tensorprodukt (eines Tensors mit einem Vektor), n

es
producto tensorial (de un tensor y un vector)

ja
テンソル積, <テンソルとベクトルとの>

pl
iloczyn tensorowy (tensora i wektora)

pt
produto tensorial (de um tensor e de um vector)

sr
тензорски производ, <тензора и вектора> м јд

sv
tensorprodukt (av en tensor och en vektor)

zh
张量积, <一个张量和一个向量的>

Publication date: 2008-08
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