Difference between revisions of "Manuals/calci/ARROWHEAD"
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| Line 13: | Line 13: | ||
* & 0 & 0 & 0 & * \\ | * & 0 & 0 & 0 & * \\ | ||
\end{bmatrix}</math> | \end{bmatrix}</math> | ||
| − | *So | + | *So Calci displays, the elements of the arrowhead matirx are 1 except 1st row and column and main diagonal. |
*The matrix has the form Any symmetric permutation of the arrowhead matrix, where P is a permutation matrix is a arrowhead matrix. | *The matrix has the form Any symmetric permutation of the arrowhead matrix, where P is a permutation matrix is a arrowhead matrix. | ||
*i.e.,<math>P^T A P</math> where P is a permutation matrix is a arrowhead matrix. | *i.e.,<math>P^T A P</math> where P is a permutation matrix is a arrowhead matrix. | ||
*Real symmetric arrowhead matrices are often an essential tool for the computation of the eigenvalues | *Real symmetric arrowhead matrices are often an essential tool for the computation of the eigenvalues | ||
| + | |||
| + | ==Examples== | ||
| + | *MATRIX("arrowhead") | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 1 || 1 || 1 | ||
| + | |- | ||
| + | | 1 || 1 || 0 | ||
| + | |- | ||
| + | | 1 || 0 || 1 | ||
| + | |} | ||
| + | *MATRIX("arrowhead",5) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 1 || 1 || 1 || 1 || 1 | ||
| + | |- | ||
| + | | 1 || 1 || 0 || 0 ||0 | ||
| + | |- | ||
| + | | 1 || 0 || 1 || 0 || 0 | ||
| + | |- | ||
| + | | 1 || 0 || 0 || 1 || 0 | ||
| + | |- | ||
| + | | 1 || 0 || 0 || 0 ||1 | ||
| + | |} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/ANTIDIAGONAL| ANTIDIAGONAL]] | ||
| + | |||
| + | ==References== | ||
Revision as of 08:37, 17 April 2015
MATRIX("ARROEHEAD",order)
- 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 order} is the order of the arrowhead matrix.
Description
- This function returns the matrix with the type arrowhead.
- In mathematical, a square matrix containing zeros in all entries except for the first row first column and main diagonal.
- i.e., The matrix of the form
A= 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{bmatrix} * & * & *& * & * \\ * & * & 0 & 0 & 0 \\ * & 0 & * & 0 & 0 \\ * & 0 & 0 & * & 0 \\ * & 0 & 0 & 0 & * \\ \end{bmatrix}}
- So Calci displays, the elements of the arrowhead matirx are 1 except 1st row and column and main diagonal.
- The matrix has the form Any symmetric permutation of the arrowhead matrix, where P is a permutation matrix is a arrowhead matrix.
- i.e.,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 P^T A P} where P is a permutation matrix is a arrowhead matrix.
- Real symmetric arrowhead matrices are often an essential tool for the computation of the eigenvalues
Examples
- MATRIX("arrowhead")
| 1 | 1 | 1 |
| 1 | 1 | 0 |
| 1 | 0 | 1 |
- MATRIX("arrowhead",5)
| 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 1 |