Condition number

Summary

A condition number measures how much the output of a problem can change, relative to the size of a small relative change in its input. For an invertible matrix $A$ and a matrix norm, it is $\kappa(A) = \norm{A} \norm{A^{-1}}$. It bounds the relative error in the solution of $Ax = b$ caused by a relative error in $b$. A problem with a large condition number is ill-conditioned: rounding errors in the data can be strongly amplified, whatever algorithm is used.