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_xB_x & A_xB_y & A_xB_z \\ A_yB_x & A_yB_y & A_yB_z \\ A_z B_x &A_zB_y & A_zB_z \end{pmatrix}method

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