Difference between revisions of "Manuals/calci/DYADIC"

Revision as of 14:31, 3 March 2017

DYADIC(a,b)

OR VECTORDIRECTPRODUCT (a,b)

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:

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

The direct product is non-commutative (AB 6D BA).A few vector product identities are of interest

@@ Line 8: / Line 8: @@
 *In <math>VECTORDIRECTPRODUCT (a,b)</math>, <math>a</math> and <math>b</math> 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:<math>AB=AB^T</math>=
+*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:
+<math>AB=AB^T</math>=
 <math>\begin{pmatrix}
 A_x  \\
 A_y \\
 A_z
-\end{pmatrix}</math>method
+\end{pmatrix}</math><math> (B_x  B_y  B_Z)</math>method
 *The direct product is non-commutative (AB 6D BA).A few vector product identities are of interest