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It states that an inner product of a vector S and a dyad expressed as the product of vectors U and V, UV, is equal to S*UV=(S*U)V=kV where k is a scalar k=S*U. That makes perfect sense. But then it says that the result is a vector with magnitude k and direction determined by V. There was no requirement that any of these vectors were unit vectors, so wouldn't the magnitude be k|V|?

Also, when discussing tensors, is it assumed that the "product" of two tensors is the dyad product and not the inner or cross product unless so specified?