Why we use $\mathbb{R}^{m \times n}$ notation instead of $\mathbb{R}^{n \times m}$? I just realised, that I use all the time the notation $\mathbb{R}^{n \times m}$, and all books and papers use $\mathbb{R}^{m \times n}$.
$\mathbb{R}^{n \times m}$ is more sympathetic for me, because I always imagine a matrix like $\mathbb{R}^n$ $m$ times. And because we use the notation $\mathbb{R}^n$ and not $\mathbb{R}^m$, thats why I used $\mathbb{R}^{n \times m}$ all the time.
Now I think I will change my practice, because I don't want diverge from the standards, but can anybody give me a reason for this habit?

Very likely because in the alphabet, $m$ precedes $n$.
