\begin{definition}[Definition:Rank/Matrix/Definition 2]
Let $K$ be a field.
Let $\mathbf A$ be an $m \times n$ matrix over $K$.
Let $\mathbf A$ be converted to echelon form $\mathbf B$.
Let $\mathbf B$ have exactly $k$ non-zero rows.
Then the '''rank''' of $\mathbf A$, denoted $\map \rho {\mathbf A}$, is $k$.
\end{definition}