I've been trying to learn more about tensors with the help of this website, http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/documents/Tensors_TM2002211716.pdf, but its explanation on one little part about vectors has me puzzled. 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?