- #1
marschmellow
- 49
- 0
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?
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?