frank: Frank matrix
In fastmatrix: Fast Computation of some Matrices Useful in Statistics
frank R Documentation
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
fastmatrix documentation built on Oct. 12, 2023, 5:14 p.m.
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| frank | R Documentation |
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
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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