\begin{definition}[Definition:Matrix Space/Real]
Let $m, n \in \Z_{>0}$ be (strictly) positive integers.
Let $\R$ denote the set of real numbers.
The '''$m \times n$ matrix space over $\R$''' is referred to as the '''real matrix space''', and can be denoted $\map {\MM_\R} {m, n}$.
If $m = n$ then we can write $\map {\MM_\R} {m, n}$ as $\map {\MM_\R} n$.
\end{definition}