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

IEV ref102-03-48

en
scalar product, <of two tensors>
for two tensors of the second-order 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@ , scalar defined by T:S= mn T mn S nm MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadiaa=rfacaGG6a Gaa83uaiabg2da9maaqafabaGaamivamaaBaaaleaacaWGTbGaamOB aaqabaaabaGaamyBaiaad6gaaeqaniabggHiLdGccaWGtbWaaSbaaS qaaiaad6gacaWGTbaabeaaaaa@461F@

Note 1 to entry: The scalar product of two tensors is denoted by a colon (:) between the two symbols of the tensors.


fr
produit scalaire, <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@ , scalaire défini par T:S= mn T mn S nm MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadiaa=rfacaGG6a Gaa83uaiabg2da9maaqafabaGaamivamaaBaaaleaacaWGTbGaamOB aaqabaaabaGaamyBaiaad6gaaeqaniabggHiLdGccaWGtbWaaSbaaS qaaiaad6gacaWGTbaabeaaaaa@461F@

Note 1 à l'article: Le produit scalaire de deux tenseurs est indiqué par un deux-points (:) entre les deux symboles des tenseurs.


de
Sakalarprodukt (zweier Tensoren), n

es
producto escalar (de dos tensores)

ja
スカラ積, <2つのテンソルの>

pl
iloczyn skalarny (dwóch tensorów)

pt
produto escalar (de dois tensores)

sr
скаларни производ, <два тензора> м јд

sv
skalärprodukt (av två tensorer)

zh
标量积, <两个张量的>

Publication date: 2008-08
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