Definition:Condition Number

Definition

A condition number is a coefficient which measures the degree of ill-conditioning of a mathematical problem.

Examples

Coefficient Matrix

Let $\mathbf A$ be the coefficient matrix of a system of simultaneous linear equations.

A condition number for $\mathbf A$ is:

the norm of $\mathbf A$ multiplied by the norm of its inverse $\mathbf A^{-1}$

If the system of simultaneous linear equations is ill-conditioned, $\mathbf A^{-1}$ will have relatively large elements and the condition number will likewise be large.

Also see

• Results about condition number can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): condition number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): condition number