The condition number of a problem measures how strongly relative perturbations of its input can amplify relative changes in its output. For an invertible matrix and a chosen operator norm, .
For a real symmetric positive-definite matrix,It measures the sensitivity of the linear system and controls convergence bounds for iterative solvers.
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The condition number is a mathematical concept used to measure the sensitivity of the solution of a system of linear equations or an optimization problem to small changes in the input data. It provides insight into how errors or perturbations in the input can affect the output, thus giving a sense of how 'well-conditioned' or 'ill-conditioned' the problem is.