<sod>  
 ==The condition number of a matrix==<!-- This section is linked from [[Invertible matrix]] -->
 
For example, the condition number associated with the [[linear equation]] 
 ''Ax''&nbsp;=&nbsp;''b'' gives a bound on how inaccurate the solution ''x'' will be after approximate solution. Note that this is before the effects of [[round-off error]] are taken into account; conditioning is a property of the matrix, not the [[algorithm]] or [[floating point]] accuracy of the computer used to solve the corresponding system. In particular, one should think of the condition number as being (very roughly) the rate at which the solution, ''x'', will change with respect to a change in ''b''.  Thus, if the condition number is large, even a small error in ''b'' may cause a large error in ''x''. On the other hand, if the condition number is small then the error in ''x'' will not be much bigger than the error in ''b''.
 
 The condition number is defined more precisely to be the maximum ratio of the [[relative error]] in ''x'' divided by the relative error in ''b''.
 <eod> <sod> 
 ==The condition number of a matrix==<!-- This section is linked from [[Invertible matrix]] -->
 
LLL For example, the condition number associated with the [[linear equation]] 
 ''Ax''&nbsp;=&nbsp;''b'' gives a bound on how inaccurate the solution ''x'' will be after approximate solution. Note that this is before the effects of [[round-off error]] are taken into account; conditioning is a property of the matrix, not the [[algorithm]] or [[floating point]] accuracy of the computer used to solve the corresponding system. In particular, one should think of the condition number as being (very roughly) the rate at which the solution, ''x'', will change with respect to a change in ''b''.  Thus, if the condition number is large, even a small error in ''b'' may cause a large error in ''x''. On the other hand, if the condition number is small then the error in ''x'' will not be much bigger than the error in ''b''.
 
 The condition number is defined more precisely to be the maximum ratio of the [[relative error]] in ''x'' divided by the relative error in ''b''.
 <eod>