Definition:Gaussian Elimination

Definition
Let $\mathbf A$ be a matrix over a field $K$.

Let $\mathbf E$ be a reduced echelon matrix which is row equivalent to $\mathbf A$.

The Gaussian elimination method is a technique for converting $\mathbf A$ into $\mathbf E$ by means of a sequence of elementary row operations.

Also known as
Some sources refer to the technique as the Gauss elimination method.

Also defined as
Some sources do not insist that $\mathbf E$ be a reduced echelon matrix at the end of the Gaussian elimination process, but merely a echelon matrix.

Also see

 * Definition:Gauss-Jordan Elimination