Manuals/calci/ARROWHEAD

MATRIX("ARROWHEAD",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= ${\begin{bmatrix}*&*&*&*&*\\*&*&0&0&0\\*&0&*&0&0\\*&0&0&*&0\\*&0&0&0&*\\\end{bmatrix}}$

• 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.,$P^{T}AP$ 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

See Also

• ANTIDIAGONAL

References

• Arrowhead