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Index

• Getting Started

• User Guide

• Functions

• Desktop Tools and Development Environment

• Data Import and Export

• Mathematics

• Arrays and Matrices

• Basic Information

Operators

• Elementary Matrices and Arrays

• Array Operations

• Array Manipulation

• Specialized Matrices

• Linear Algebra

• Elementary Math

• Polynomials

• Interpolation and Computational Geometry

• Cartesian Coordinate System Conversion

• Nonlinear Numerical Methods

• Specialized Math

• Sparse Matrices

• Math Constants

• Data Analysis

• Programming and Data Types

• Object-Oriented Programming

• Graphics

• 3-D Visualization

• GUI Development

• External Interfaces

• Examples

• Release Notes

Learn more about MATLAB

hilb - Hilbert matrix

Syntax

H = hilb(n)

Description

H = hilb(n) returns the Hilbert matrix of order n.

Definition

The Hilbert matrix is a notable example of a poorly conditioned matrix [1]. The elements of the Hilbert matrices are .

Examples

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

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

References

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

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