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IEVref:102-03-41ID:
Language:enStatus: Standard
Term: dyadic product
Synonym1: tensor product, <of two vectors>
Synonym2:
Synonym3:
Symbol:
Definition: for two vectors U and V in an n-dimensional Euclidean space, tensor of the second order defined by the bilinear form f(X,Y)=(UX)(VY) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaaC iwaiaabYcacaaMe8UaaCywaiaacMcacqGH9aqpcaGGOaGaaCyvaiab gwSixlaahIfacaGGPaGaaiikaiaahAfacqGHflY1caWHzbGaaiykaa aa@4ADC@ , where X and Y are any vectors in the same space

Note 1 to entry: The bilinear form can be represented by f( X,Y )=( i U i X i )( j V j Y j )= ij U i V j X i Y j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaKqzafGaamOzaOWaae WaaeaacaWHybGaaiilaiaahMfaaiaawIcacaGLPaaajugqbiabg2da 9OWaaeWaaeaadaaeqbqaaiaadwfadaWgaaWcbaGaamyAaaqabaGcca WGybWaaSbaaSqaaiaadMgaaeqaaaqaaiaadMgaaeqaniabggHiLdaa kiaawIcacaGLPaaadaqadaqaamaaqafabaGaamOvamaaBaaaleaaca WGQbaabeaakiaadMfadaWgaaWcbaGaamOAaaqabaaabaGaamOAaaqa b0GaeyyeIuoaaOGaayjkaiaawMcaaiabg2da9maaqafabaGaamyvam aaBaaaleaacaWGPbaabeaaaeaacaWGPbGaamOAaaqab0GaeyyeIuoa kiaadAfadaWgaaWcbaGaamOAaaqabaGccaWGybWaaSbaaSqaaiaadM gaaeqaaOGaamywamaaBaaaleaacaWGQbaabeaaaaa@5AC2@ in terms of the coordinates of the vectors. The dyadic product is then the tensor with components T ij = U i V j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadsfadaWgaaWcba qcLboacaWGPbGaamOAaaWcbeaakiabg2da9KqzafGaamyvaOWaaSba aSqaaKqzGdGaamyAaaWcbeaajugqbiaadAfakmaaBaaaleaajug4ai aadQgaaSqabaaaaa@4626@ .

Note 2 to entry: The dyadic product of two vectors is denoted by UV MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfacqGHxkcXca WHwbaaaa@3C93@ or UV MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfacaWHwbaaaa@3A8A@ .


Publication date:2008-08
Source:
Replaces:
Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
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