matrixcalc (version 1.0-3)

hilbert.matrix: Hilbert matrices

Description

This function returns an n by n Hilbert matrix.

Usage

hilbert.matrix(n)

Arguments

n

Order of the Hilbert matrix

Value

A matrix.

Details

A Hilbert matrix is an order \(n\) square matrix of unit fractions with elements defined as \(H_{i,j} = {1 \mathord{\left/ {\vphantom {1 {\left( {i + j - 1} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {i + j - 1} \right)}}\).

References

Hilbert, David (1894). Ein Beitrag zur Theorie des Legendre schen Polynoms, Acta Mathematica, Springer, Netherlands, 18, 155-159.

Examples

# NOT RUN {
H <- hilbert.matrix( 4 )
print( H )
# }