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 decomposition]?s, polynomial root finding,
eigenvalue and many other problems may be defined.