Manuals/calci/ARROWHEAD
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MATRIX("ARROWHEAD",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
- MATRIX("arrowhead",3)
| 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 |