Hilbert matrix

1 Hilbert Matrix

A Hilbert matrixMathworldPlanetmath H of order n is a square matrixMathworldPlanetmath defined by


An example of a Hilbert matrix when n=5 is


Hilbert matrices are ill-conditioned.

2 Inverse

The inverse of a Hilbert matrix H-1MN() is given by


An example of an inverted Hilbert matrix when n=5 case is:


For more fun with Hilbert matrices, see [1].


  • 1 Choi, Man-Duen. Tricks or Treats with the Hilbert Matrix. American Mathematical Monthly 90, 301-312, 1983.
Title Hilbert matrix
Canonical name HilbertMatrix
Date of creation 2013-03-22 13:04:14
Last modified on 2013-03-22 13:04:14
Owner Daume (40)
Last modified by Daume (40)
Numerical id 6
Author Daume (40)
Entry type Definition
Classification msc 15A57
Classification msc 15A09
Classification msc 15A12
Classification msc 65F35