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tensor prodcut and scalar product and inner produc

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Old   April 4, 2006, 00:18
Default tensor prodcut and scalar product and inner produc
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ztdep
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what is the difference between these three product! regards
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Old   April 4, 2006, 07:44
Default Re: tensor prodcut and scalar product and inner pr
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Karsten
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Since this is a very basic question i guess you will find your answers in the web, for example: http://en.wikipedia.org/wiki/Tensor_product http://en.wikipedia.org/wiki/Dot_product http://en.wikipedia.org/wiki/Inner_product_space
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Old   April 4, 2006, 10:41
Default Re: tensor prodcut and scalar product and inner pr
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Darko Matovic
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Tensor product (also called the outer product) increases the tensor order. I.e. a tensor product of two vectors (i.e. first order tensors) creates a second order tensor - two single-index entities generate a double index entity. Tensor prod. of two 2nd order tensors creates a 4th order tensor, etc. Scalar product and inner product are the same, they reduce the tensor order. Thus two 1st order tensors (vectors) create a scalar. In Einstein notation it is indicated by a repeated index. I.e. the production and the dissipation terms in the turbulence intensity equation are inner products with double repeated indices, which reduce product of deformation tensors (2nd order tensors) to a scalar.
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