Description

This function returns an order n Frobenius matrix that is useful in numerical mathematics.

Usage

Arguments

Details

The Frobenius matrix is also called the companion matrix. It arises in the solution of systems of linear first order differential equations. The formula for the order n Frobenius matrix is {\bf{F}} = ≤ft[ {\begin{array}{*{20}{c}}0&0& \cdots &0&{{{≤ft( { - 1} \right)}^{n - 1}} ≤ft( {\begin{array}{*{20}{c}}n\\0\end{array}} \right)}\\1&0& \cdots &0&{{{≤ft( { - 1} \right)}^{n - 2}} ≤ft( {\begin{array}{*{20}{c}}n\\1\end{array}} \right)}\\0&1& \ddots &0&{{{≤ft( { - 1} \right)}^{n - 3}} ≤ft( {\begin{array}{*{20}{c}}n\\2\end{array}} \right)}\\ \vdots & \vdots & \ddots & \vdots & \vdots \\0&0& \cdots &1&{{{≤ft( { - 1} \right)}^0} ≤ft( {\begin{array}{*{20}{c}}n\\{n - 1}\end{array}} \right)}\end{array}} \right].

Value

An order n matrix

Note

If the argument n is not a positive integer that is greater than 1, the function presents an error message and stops.

Author(s)

Frederick Novomestky fnovomes@poly.edu

References

Aceto, L. and D. Trigiante (2001). Matrices of Pascal and Other Greats, American Mathematical Monthly, March 2001, 108(3), 232-245.

Examples