Given vectors 
and 
, the vector direct product, also known as a dyadic,
is
 |
where 
is the Kronecker product and 
is the matrix transpose.
For the direct product of two 3-vectors,
![uv=[u_1v^T; u_2v^T; u_3v^T]=[u_1v_1 u_1v_2 u_1v_3; u_2v_1 u_2v_2 u_2v_3; u_3v_1 u_3v_2 u_3v_3].](/images/equations/VectorDirectProduct/NumberedEquation2.svg) |
Note that if 
,
then 
,
where 
is the Kronecker delta.
Vector Direct Product
See also
Dyadic, Kronecker Product, Sherman-Morrison Formula, Woodbury FormulaExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Vector Direct Product." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VectorDirectProduct.html