frank {fastmatrix}R Documentation

Frank matrix

Description

This function returns the Frank matrix of order nn.

Usage

frank(n = 1)

Arguments

n

order of the Frank matrix.

Details

A Frank matrix of order nn is a square matrix Fn=(fij)\bold{F}_n = (f_{ij}) defined as

fij={nj+1,ij,nj,i=j+1,0,ij+2f_{ij} = \left\{ {\begin{array}{ll} n - j + 1, & i \le j, \\ n - j, & i = j + 1, \\ 0, & i \ge j + 2 \end{array}} \right.

Value

Returns an nn by nn matrix.

References

Frank, W.L. (1958). Computing eigenvalues of complex matrices by determinant evaluation and by methods of Danilewski and Wielandt. Journal of the Society for Industrial and Applied Mathematics 6, 378-392.

Examples

F5 <- frank(n = 5)
det(F5) # equals 1

[Package fastmatrix version 0.5-772 Index]