# hilb

## Purpose

Hilbert matrix.

## Synopsis

    H = hilb(n)

## Description

`hilb(n)` returns the Hilbert matrix of order `n`. The elements of the Hilbert matrices are

The Hilbert matrix is a notable example of a poorly conditioned matrix [1].

## Examples

Even the fourth order Hilbert matrix shows signs of poor conditioning.

    cond(hilb(4)) =

        1.5514e+04

## Algorithm

See the M-file for a good example of efficient MATLAB programming where conventional `for` loops are replaced by vectorized statements.

## See Also

    invhilb

## References

[1] G. E. Forsythe and C. B. Moler, Computer Solution of Linear Algebraic Systems, Chapter 19, Prentice-Hall, 1967.

(c) Copyright 1994 by The MathWorks, Inc.