Editing Kernel (linear algebra) (section)

===Exact coefficients===
If the coefficients of the matrix are exactly given numbers, the [[column echelon form]] of the matrix may be computed with [[Bareiss algorithm]] more efficiently than with Gaussian elimination. It is even more efficient to use [[modular arithmetic]] and [[Chinese remainder theorem]], which reduces the problem to several similar ones over [[finite field]]s (this avoids the overhead induced by the non-linearity of the [[computational complexity]] of integer multiplication).{{Citation needed|date=October 2014}}

For coefficients in a finite field, Gaussian elimination works well, but for the large matrices that occur in [[cryptography]] and [[Gröbner basis]] computation, better algorithms are known, which have roughly the same [[Analysis of algorithms|computational complexity]], but are faster and behave better with modern [[computer hardware]].{{Citation needed|date=October 2014}}