Manuals/calci/DYADIC

DYADIC(a,b)

OR VECTORDIRECTPRODUCT (a,b)

$a$ and $b$ any two set of values.

Description

This function shows the Vector Direct product.
The third type of vector multiplication is called the direct product, and is written AB.
In $VECTORDIRECTPRODUCT(a,b)$ , $a$ and $b$ are the two vectors.
Multiplying one vector by another under the direct product gives a tensor result.
The rectangular components of the direct product may be found by matrix multiplication: one multiplies the column vector A by the transpose of B, which gives a 3X3 matrix:

$AB=AB^{T}$ = ${\begin{pmatrix}A_{x}\\A_{y}\\A_{z}\end{pmatrix}}$ $(B_{x}B_{y}B_{Z})$ = ${\begin{pmatrix}A_{x}B_{x}&A_{x}B_{y}&A_{x}B_{z}\\A_{y}B_{x}&A_{y}B_{y}&A_{y}B_{z}\\A_{z}B_{x}&A_{z}B_{y}&A_{z}B_{z}\end{pmatrix}}$