Condition number

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The condition number associated with a mathematical structure is a measure of that quantities amenability to digital computation. For example, the condition number associated with the linear equation Ax = b controls how accurate the solution x will be after numerical solution. Condition number also amplifies the error present in b. The extent of this amplification can render a low condition number system (normally a good thing) inaccurate and a high condition number system (normally a bad thing) accurate, depending on how well the data in b are known. For this problem, the condition number is defined by ||A^{-1}||.||A||, in any consistent norm.

Condition numbers for singular value decompositions, polynomial root finding, eigenvalue and many other problems may be defined.