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Tensors, dyads, triads

  1. Jul 14, 2010 #1
    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/Numbers/Math/documents/Tensors_TM2002211716.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.

    Last edited: Jul 14, 2010
  2. jcsd
  3. Jul 14, 2010 #2
    I changed the initial post quite a bit and am bumping it in order to gain more views.
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