This function returns the Frank matrix of order \(n\).
Usage
frank(n = 1)
Value
Returns an \(n\) by \(n\) matrix.
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
$$f_{ij} = \left\{ {\begin{array}{ll}
n - j + 1, & i \le j, \\
n - j, & i = j + 1, \\
0, & i \ge j + 2
\end{array}} \right.$$
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 Mathematics6, 378-392.