I am reading the following document entitled: An Introduction to Tensors for Students of Physics and Engineering. This document can be found at the following link: http://www.grc.nasa.gov/WWW/k-12/Num...2002211716.pdf
Specifically, I am having trouble with page 11 on the paragraph right after the bolded and centered Tensors of Rank > 2.
This paragraph states that:Tensors of rank 2 result from dyad products of vectors. (This I have no problem with, as I am familiar with this type of vector multiplication, especially in R^3. Since it produces the familiar 3x3 matrix from the product of v(v^T), with v a 1x3 vector). However, I am having problems with the next sentence which reads: In an entirely analogous way, tensors of
rank 3 arise from triad products, UVW (U,V,W vectors), and tensors of rank n arise from “n-ad” products of
vectors, UVW...AB.
I would like to know how to compute a triad product resulting in a tensor of rank 3 from 3 given vectors (an example would be great as this document does not have any). Also, if it is no trouble an example of an "n-ad" product of vectors UVW...AB would be very much appreciated but only necessary if it follows a different pattern than that of a triad product.
Thanks