IEC 60050 - International Electrotechnical Vocabulary


IEVref:	102-03-48		ID:
Language:	en		Status: Standard

Term:	scalar product, <of two tensors>
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Definition:	for two tensors of the second-order $T = (T_{i j})$ and $S = (S_{k l})$ , scalar defined by $T : S = \sum_{m n} T_{m n} S_{n m}$ Note 1 to entry: The scalar product of two tensors is denoted by a colon (:) between the two symbols of the tensors.
Publication date:	2008-08
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Internal notes:	2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
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T=( T ij ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadKqzGfGaa8hvaO Gaeyypa0JaaiikaiaadsfadaWgaaWcbaGaamyAaiaadQgaaeqaaOGa aiykaaaa@3C54@ S=( S kl ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaGqadiaa=nfacqGH9a qpcaGGOaGaam4uamaaBaaaleaacaWGRbGaamiBaaqabaGccaGGPaaa aa@3B7D@ 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.