# Manuals/calci/HILBERT

MATRIX("HILBERT",order)

• is the order of the Hilbert matrix.

## Description

• This function gives matrix of order 3x3 with the property of Hilbert.
• A Hilbert matrix, is a square matrix with entries being the unit fractions. i.e.,.
• The Hilbert matrix is an example of a Hankel matrix.
• The Hilbert matrix is symmetric and positive definite.
• Also Hilbert matrices are canonical examples of ill-conditioned matrices, making them notoriously difficult to use in numerical computation.
• Here MATRIX("hilbert") gives the hilbert matrices with a decimal places .
• i.e., For 1/2 it will show 0.5, 1/3 will show 0.333 and so on.

## Examples

• 1.MATRIX("hilbert")= 1
• 2.MATRIX("hilbert",3)
 1 0.5 0.333333 0.5 0.333333 0.25 0.333333 0.25 0.2
• 3.MATRIX("hilbert",5)
 1 0.5 0.333333 0.25 0.2 0.5 0.333333 0.25 0.2 0.166667 0.333333 0.25 0.2 0.166667 0.142857 0.25 0.2 0.166667 0.142857 0.125 0.2 0.166667 0.142857 0.125 0.111111

Hilbert Matrix