Difference between revisions of "Manuals/calci/DYADIC"
| Line 14: | Line 14: | ||
A_y \\ | A_y \\ | ||
A_z | A_z | ||
| − | \end{pmatrix}</math><math> (B_x B_y B_Z)</math>=\begin{pmatrix} | + | \end{pmatrix}</math><math> (B_x B_y B_Z)</math>=<math>\begin{pmatrix} |
A_xB_x & A_xB_y & A_xB_z \\ | A_xB_x & A_xB_y & A_xB_z \\ | ||
A_yB_x & A_yB_y & A_yB_z \\ | A_yB_x & A_yB_y & A_yB_z \\ | ||
A_z B_x &A_zB_y & A_zB_z | A_z B_x &A_zB_y & A_zB_z | ||
| − | \end{pmatrix}method | + | \end{pmatrix}</math>method |
*The direct product is non-commutative (AB 6D BA).A few vector product identities are of interest | *The direct product is non-commutative (AB 6D BA).A few vector product identities are of interest | ||
Revision as of 14:36, 3 March 2017
OR VECTORDIRECTPRODUCT (a,b)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle VECTORDIRECTPRODUCT (a,b)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle AB=AB^T} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{pmatrix} A_x \\ A_y \\ A_z \end{pmatrix}} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (B_x B_y B_Z)} =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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