IEC 60050 - International Electrotechnical Vocabulary


IEVref:	102-03-45		ID:
Language:	en		Status: Obsolete

Term:	inner product (of two tensors)
Synonym1:	contracted product (of two tensors) [Preferred]
Synonym2:
Synonym3:
Symbol:
Definition:	for two second-order tensors $T = (T_{i j})$ and $S = (S_{k l})$ , tensor of the second order the components of which are given by ${(T \cdot S)}_{i l} = \sum_{m} T_{i m} S_{m l}$ NOTE The inner product is denoted by a half-high dot (·) between the two symbols representing the tensors.
Publication date:	2007-08
Source
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Internal notes:	2017-06-02: Cleanup - Remove Attached Image 102-03-45en.gif
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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) 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 The inner product is denoted by a half-high dot (·) between the two symbols representing the tensors.