Definition:Matrix Space/Real

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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 $\map {\MM_\R} n$.

Also denoted as

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

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

  • $\map {M_{m, n} } \R$
  • $\R^{m \times n}$

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

  • $\map {M_n} \R$
  • $\R^{n \times n}$

with varying styles of $\MM$.