<sod> The <b>condition number</b> associated with a mathematical structure is a measure of that quantity's 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. <eod> <sod>The <b>condition number</b> associated with a numerical problem is a measure of 
that quantity's amenability to digital computation, that is, how
[[well-posed problem|well-posed]] the problem is.

For example, the condition number associated with the linear equation 
<math>Ax = b</math> gives a bound on how inaccurate the solution <math>x</math> will be after numerical solution.  

The condition number also amplifies the error present in <math>b</math>.   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 <math>b</math> are known.  For this problem, the condition number is defined by 

<math>||A^{-1}||.||A||</math>, 

in any consistent [[norm]].
 
 Condition numbers for [[singular value decomposition]]s, polynomial root finding, 
 [[eigenvalue]] and many other problems may be defined. <eod>