TITLE: What is the notation for the set of all $m\times n$ matrices?
QUESTION [18 upvotes]: Given that $\mathbb{R}^n$ is the notation used for n-dimensional vectors, is there an accepted equivalent notation for matrices?

REPLY [2 votes]: The notation $A\in\mathbb{R}^{m\times n}$ is in fact correct. We should be careful with the symbol '$\times$' that in this case does not means an integer product but a group product that, as a result, is a new group in $\mathbb{R}^2$ with elements of the form $(m, n)$, and thus the matrix $A$ is contained in it.