| creation.matrix {matrixcalc} | R Documentation |
Creation Matrix
Description
This function returns the order n creation matrix, a square matrix with the sequence 1, 2, ..., n - 1 on the sub-diagonal below the principal diagonal.
Usage
creation.matrix(n)
Arguments
n |
a positive integer greater than 1 |
Details
The order n creation matrix is also called the derivation matrix and is
used in numerical mathematics and physics. It arises in the solution of linear
dynamical systems. The form of the matrix is
\left\lbrack {\begin{array}{cccccc}
0&0&0& \cdots &0&0\\
1&0&0& \cdots &0&0\\
0&2&0& \cdots &0&0\\
0&0&3& \ddots &0&0\\
\vdots & \vdots & \vdots & \ddots & \ddots &{}\\
0&0&0& \cdots &{n - 1}&0
\end{array}} \right\rbrack.
Value
An order n matrix.
Note
If the argument n is not an 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.
Weinberg, S. (1995). The Quantum Theory of Fields, Cambridge University Press.
Examples
H <- creation.matrix( 10 )
print( H )