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The condition number of matrix measures how close it is to being singular

Created over 8 years ago, updated 10 days ago

Definition: The condition number of a nonsingular matrix $A$ is $\kappa(A) = \|A\| \cdot \|A^{-1}\|$. For the 2-norm, $\kappa(A) = \sigma_{\max}/\sigma_{\min}$ (ratio of largest to smallest singular value). A large condition number indicates the matrix is close to singular and numerical computations will be unstable.