matrixcalc (version 1.0-3)

pascal.matrix: Pascal matrix

Description

This function returns an n by n Pascal matrix.

Usage

pascal.matrix(n)

Arguments

n

Order of the matrix

Value

An order \(n\) 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.

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

# NOT RUN {
P <- pascal.matrix( 4 )
print( P )
# }