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

IEV ref102-03-45

en
inner product, <of two tensors>
contracted product, <of two tensors>
for two second-order tensors T=( T ij ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadKqzGfGaa8hvaO Gaeyypa0JaaiikaiaadsfadaWgaaWcbaGaamyAaiaadQgaaeqaaOGa aiykaaaa@3C54@ and S=( S kl ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadiaa=nfacqGH9a qpcaGGOaGaam4uamaaBaaaleaacaWGRbGaamiBaaqabaGccaGGPaaa aa@3B7D@ , tensor of the second order the components of which are given by (TS) il = m T im S ml MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaacIcaieWacaWFub GaeyyXICTaa83uaiaacMcadaWgaaWcbaGaamyAaiaadYgaaeqaaOGa eyypa0ZaaabuaeaacaWGubWaaSbaaSqaaiaadMgacaWGTbaabeaaae aacaWGTbaabeqdcqGHris5aOGaam4uamaaBaaaleaacaWGTbGaamiB aaqabaaaaa@4A20@

Note 1 to entry: The inner product is denoted by a half-high dot (·) between the two symbols representing the tensors.


fr
produit intérieur, <de deux tenseurs> m
produit contracté, <de deux tenseurs> m
pour deux tenseurs du deuxième ordre T=( T ij ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadKqzGfGaa8hvaO Gaeyypa0JaaiikaiaadsfadaWgaaWcbaGaamyAaiaadQgaaeqaaOGa aiykaaaa@3C54@ et S=( S kl ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadiaa=nfacqGH9a qpcaGGOaGaam4uamaaBaaaleaacaWGRbGaamiBaaqabaGccaGGPaaa aa@3B7D@ , tenseur du deuxième ordre dont les coordonnées sont (TS) il = m T im S ml MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaacIcaieWacaWFub GaeyyXICTaa83uaiaacMcadaWgaaWcbaGaamyAaiaadYgaaeqaaOGa eyypa0ZaaabuaeaacaWGubWaaSbaaSqaaiaadMgacaWGTbaabeaaae aacaWGTbaabeqdcqGHris5aOGaam4uamaaBaaaleaacaWGTbGaamiB aaqabaaaaa@4A20@

Note 1 à l'article: Le produit intérieur de deux tenseurs est indiqué par un point à mi-hauteur (·) entre les deux symboles représentant les tenseurs.


de
inneres Produkt (zweier Tensoren), n

es
producto interior (de dos tensores)

ja
内積, <2つのテンソルの>
縮約積, <2つのテンソルの>

pl
iloczyn wewnętrzny (dwóch tensorów)
iloczyn przez kontrakcję (dwóch tensorów)

pt
produto interior (de dois tensores)
produto contratado (de dois tensores)

sr
унутрашњи производ, <два тензора> м јд
скраћени производ, <два тензора> м јд

sv
inre produkt (av två tensorer)
inre produkt av två tensorer

zh
内积, <两个张量的>
收缩积, <两个张量的>

Publication date: 2008-08
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