This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.


Hilbert matrix


H = hilb(n)
H = hilb(n,classname)



H = hilb(n) returns the Hilbert matrix of order n. The Hilbert matrix is a notable example of a poorly conditioned matrix. The elements of Hilbert matrices are given by H(i,j) = 1/(i + j – 1).

H = hilb(n,classname) returns a matrix of class classname, which can be either 'single' or 'double'.


collapse all

Compute the fourth-order Hilbert matrix and its condition number to see that it is poorly conditioned.

H = hilb(4)
H = 4×4

    1.0000    0.5000    0.3333    0.2500
    0.5000    0.3333    0.2500    0.2000
    0.3333    0.2500    0.2000    0.1667
    0.2500    0.2000    0.1667    0.1429

ans = 1.5514e+04

Input Arguments

collapse all

Matrix order, specified as a scalar, nonnegative integer.

Example: hilb(10)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Matrix class, specified as either 'double' or 'single'.

Example: hilb(10,'single')

Data Types: char


[1] Forsythe, G. E. and C. B. Moler. Computer Solution of Linear Algebraic Systems. Englewood Cliffs, NJ: Prentice-Hall, 1967.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

Introduced before R2006a