| pascal.matrix {matrixcalc} | R Documentation |
Pascal matrix
Description
This function returns an n by n Pascal matrix.
Usage
pascal.matrix(n)
Arguments
n |
Order of the matrix |
Details
In mathematics, particularly matrix theory and combinatorics, the Pascal matrix is a lower triangular matrix with binomial coefficients in the rows. It is easily obtained by performing an LU decomposition on the symmetric Pascal matrix of the same order and returning the lower triangular matrix.
Value
An order n matrix.
Note
If the argument n is not a positive integer, 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, 232-245.
Call, G. S. and D. J. Velleman, (1993). Pascal's matrices, American Mathematical Monthly, April 1993, 100, 372-376.
Edelman, A. and G. Strang, (2004). Pascal Matrices, American Mathematical Monthly, 111(3), 361-385.
See Also
lu.decomposition,
symmetric.pascal.matrix
Examples
P <- pascal.matrix( 4 )
print( P )