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