Definition:Matrix Space/Complex

Definition
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 $\map {\MM_\C} n$.

Also denoted as
Various forms of $\MM$ may be used; $\mathbf M$ and $M$ being common.

Some sources denote $\map {\MM_\C} {m, n}$ as:


 * $\map {M_{m, n} } \C$
 * $\C^{m \times n}$

Similarly, $\map {\MM_\C} n$ can be seen as:


 * $\map {M_n} \C$
 * $\C^{n \times n}$

with varying styles of $\MM$.