I've been studying numerical methods for solving systems of equations, and I came across the concept of the condition number for linear systems. I understand that the condition number is used to measure the sensitivity of the solution to small changes in the input data, and that a high condition number indicates an ill-conditioned system.
However, I'm not sure how to extend this concept to non-linear systems. Can anyone explain the relation between condition numbers and non-linear systems? How can I compute the condition number for a non-linear system? Any references or examples would be greatly appreciated.