Difference between revisions of "Manuals/calci/ARROWHEAD"
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*This function returns the matrix with the type arrowhead. | *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. | *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 | + | *i.e., The matrix of the form |
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A= <math>\begin{bmatrix} | A= <math>\begin{bmatrix} | ||
* & * & *& * & * \\ | * & * & *& * & * \\ | ||
* & * & 0 & 0 & 0 \\ | * & * & 0 & 0 & 0 \\ | ||
| − | * & 0 & * & 0 & 0 \\ | + | * & 0 & * & 0 & 0 \\ |
| + | * & 0 & 0 & * & 0 \\ | ||
| + | * & 0 & 0 & 0 & * \\ | ||
\end{bmatrix}</math> | \end{bmatrix}</math> | ||
*So in Calci, the elements of the arrowhead matirx are 1 except 1st row and column and main diagonal. | *So in Calci, 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.,P^T A P 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 | ||
Revision as of 09:25, 17 April 2015
MATRIX("ARROEHEAD",order)
- is the order of the arrowhead matrix.
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=
- So in Calci, 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., 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
where P is a permutation matrix is a arrowhead matrix.