The ratio of the largest to smallest singular value in the singular value decomposition of a matrix. The base- logarithm of is an estimate of how many base- digits are lost in solving a linear system with that matrix. In other words, it estimates worst-case loss of precision. A system is said to be singular if the condition number is infinite, and ill-conditioned if it is too large, where "too large" means roughly the precision of matrix entries.

An estimate of the -norm
condition number of a matrix can be computed in the Wolfram
Language prior to Version 11.2 using `LinearAlgebra`MatrixConditionNumber`[*m*,
*p*] for ,
2, or ,
where omitting the
is equivalent to specifying `Infinity`. A similar approximation for the condition number can be computed
using `LUDecomposition`[*mat*][[-1]].