Difference between revisions of "Manuals/calci/DYADIC"
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*In <math>VECTORDIRECTPRODUCT (a,b)</math>, <math>a</math> and <math>b</math> are the two vectors. | *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. | *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>=\begin{pmatrix} | + | *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_x \\ | ||
A_y \\ | A_y \\ | ||
A_z | A_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 14:30, 3 March 2017
DYADIC(a,b)
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 \begin{pmatrix} A_x \\ A_y \\ A_z \end{pmatrix}} method
- The direct product is non-commutative (AB 6D BA).A few vector product identities are of interest