Difference between revisions of "Manuals/calci/ARROWHEAD"

Revision as of 08:23, 17 April 2015

MATRIX("ARROEHEAD",order)

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= [* * * * *

      * * 0 0 0
      * 0 * 0 0
      * 0 0 * 0
      * 0 0 0 *].

A= ${\begin{bmatrix}*&*&*&*&*\\*&*&0&0&0\\*&0&*&0&0\\\end{bmatrix}}$

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.,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

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''ARROWHEAD'''</div><br/>
+<div style="font-size:30px">'''MATRIX("ARROEHEAD",order)'''</div><br/>
+*<math>order</math> 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= [* * * * *
+       * * 0 0 0
+       * 0 * 0 0
+       * 0 0 * 0
+       * 0 0 0 *].
+A= <math>\begin{bmatrix}
+*  & * & *& * & *  \\
+* & * & 0 & 0 & 0 \\
+* & 0 & * & 0 & 0 \\
+\end{bmatrix}</math>
+*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.,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