Condition Number


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.