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

IEV ref102-03-44

en
tensor product, <of two tensors>
tensor of the fourth order defined by the four-linear form equal to the product of the bilinear forms defining two tensors of the second order on the same Euclidean space

Note 1 to entry: The components of the tensor product of the tensors T and S are: (TS) ijkl = T ij S kl MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaaiikaGqadi aa=rfacqGHxkcXcaWFtbGaaiykaOWaaSbaaSqaaiaadMgacaWGQbGa am4AaiaadYgaaeqaaOGaeyypa0tcLbuacaWGubGcdaWgaaWcbaGaam yAaiaadQgaaeqaaOGaam4uamaaBaaaleaacaWGRbGaamiBaaqabaaa aa@46A3@ .

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


fr
produit tensoriel, <de deux tenseurs> m
tenseur du quatrième ordre défini par la forme quadrilinéaire égale au produit des formes bilinéaires qui définissent deux tenseurs du deuxième ordre sur le même espace euclidien

Note 1 à l'article: Les coordonnées du produit tensoriel des tenseurs T et S sont: (TS) ijkl = T ij S kl MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaaiikaGqadi aa=rfacqGHxkcXcaWFtbGaaiykaOWaaSbaaSqaaiaadMgacaWGQbGa am4AaiaadYgaaeqaaOGaeyypa0tcLbuacaWGubGcdaWgaaWcbaGaam yAaiaadQgaaeqaaOGaam4uamaaBaaaleaacaWGRbGaamiBaaqabaaa aa@46A3@ .

Note 2 à l'article: Le produit tensoriel de deux tenseurs est noté TS MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadKqzafGaa8hvai abgEPielaa=nfaaaa@39BC@ .


de
Tensorprodukt (zweier Tensoren), n

es
producto tensorial (de dos tensores)

ja
テンソル積, <2つのテンソルの>

pl
iloczyn tensorowy (dwóch tensorów)

pt
produto tensorial (de dois tensores)

sr
тензорски производ, <два тензора> м јд

sv
tensorprodukt (av två tensorer)

zh
张量积, <两个张量的>

Publication date: 2008-08
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