Manuals/calci/ARROWHEAD

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	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