Definition. The condition number of a nonsingular matrix A with respect to a matrix norm is ||A|| ||A-1||. It is a measure of the sensitivity of the solution of Ax=b to perturbations of A or b. If the condition number of A is `large', A is said to be ill-conditioned. If the condition number is near one, A is said to be well-conditioned If the condition number is one, A is said to be perfectly conditioned.