The ratio C of the largest to smallest singular value in the singular value decomposition of a matrix. The base-b logarithm of C is an estimate of how many base-b 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 log(C)≳ the precision of matrix entries.

ill-conditioned matrix | singular matrix | singular value | singular value decomposition