Editing Rank (linear algebra) (section)

=== Computation ===
When applied to [[floating point]] computations on computers, basic Gaussian elimination ([[LU decomposition]]) can be unreliable, and a rank-revealing decomposition should be used instead. An effective alternative is the [[singular value decomposition]] (SVD), but there are other less computationally expensive choices, such as [[QR decomposition]] with pivoting (so-called [[rank-revealing QR factorization]]), which are still more numerically robust than Gaussian elimination. Numerical determination of rank requires a criterion for deciding when a value, such as a singular value from the SVD, should be treated as zero, a practical choice which depends on both the matrix and the application.