Editing Gaussian elimination (section)

=== Numeric instability ===
One possible problem is [[numerical stability|numerical instability]], caused by the possibility of dividing by very small numbers. If, for example, the leading coefficient of one of the rows is very close to zero, then to row-reduce the matrix, one would need to divide by that number. This means that any error which existed for the number that was close to zero would be amplified. Gaussian elimination is numerically stable for [[diagonally dominant]] or [[Positive-definite matrix|positive-definite]] matrices. For general matrices, Gaussian elimination is usually considered to be stable, when using [[Pivot element#Partial and complete pivoting|partial pivoting]], even though there are examples of stable matrices for which it is unstable.<ref>{{harvnb|Golub|Van Loan|1996|at=§3.4.6}}</ref>