hilb

Purpose

Hilbert matrix.

H = hilb(n)

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].

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

cond(hilb(4)) =
          
    1.5514e+04

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

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