tensor prodcut and scalar product and inner produc
 

what is the difference between these three product! regards

Re: tensor prodcut and scalar product and inner pr
 

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

Re: tensor prodcut and scalar product and inner pr
 

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.