Condition Number

A scalar quantifying sensitivity of the solution of a problem to perturbations in input; for an invertible matrix A and a chosen norm, the matrix condition number is κ(A) = ||A|| · ||A^{-1}|| and measures worst-case relative amplification of errors.

A scalar quantity that measures how relative perturbations in the input data of a problem are amplified into relative perturbations in its solution; for a linear system Ax = b with invertible A and a chosen norm, the matrix condition number is ||A||·||A^{-1}||.

A numerical measure of how sensitively the output of a function or solution of a linear system responds to small relative perturbations of the input; for invertible matrices under a chosen norm it is typically ||A|| ||A^{-1}||, and for matrices equals the ratio of largest to smallest singular value in the spectral norm.