frank {fastmatrix}

Frank matrix

Description

This function returns the Frank matrix of order n.

Usage

frank(n = 1)

Arguments

n

order of the Frank matrix.

Details

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

f_{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 n by n 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