User:Nikita2/sandbox2

Condition number of square matrix $A$ is defined as \begin{equation} \kappa(A) = \|A\|_2\cdot\|A^{-1}\|_2. \end{equation} If A is singular matrix ( degenerate matrix ) $\kappa(A)=\infty$. Condition number of matrix $A$ is a way of describing how well or bad the system $Ax=b$ could be approximated. If $\kappa(A)$ is small the problem is well-conditioned and if $\kappa(A)$ is large the problem is rather ill-conditioned.