Manuals/calci/ARROWHEAD

MATRIX("ARROEHEAD",order)

• $order$ 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= [* * * * *

      * * 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