\begin{definition}[Definition:Gaussian Elimination]
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.
\end{definition}