How to express the size of a dimension of a matrix Let's say I have a matrix $A\in \mathbb{C}^{4\times6}$.
How can I express mathematically that I want to input $A$ and output $4$ as an answer, for example?
In code we might do size(A), A.shape, A.RowCount(), depending on the computer language we are using. But what about in math?
Note that putting $A_{4\times 6}$ is not what I'm looking for because $4$ or $6$ is the desired answer, not part of the formula for finding the answer. And putting $A_{m\times n}$ doesn't derive the answer either; it just states $A$ has dimensions $m$ and $n$.
Update
I found this, if this gives anyone any ideas. It gets the columns.
$\text{rk}(A)+\text{nul}(A)=n$, given $A\in \mathbb{C}^{m\times n}$.
Update 2
I decided to use $\#_1 A$ for the row count and $\#_2 A$ for the column count. I welcome feedback as to why that would confuse mathematicians who may read my notebook.

You would say that's the number of rows of the matrix $A$.
EDIT: If roundabout ways are okay, one route is to identify a $m\times n$ matrix $M$ as some linear transformation $T:\mathbb{R}^n\longrightarrow\mathbb{R}^m$.
Then we can say $\dim(\text{Codomain}(M))=m$ and $\dim(\text{Domain}(M))=n$.
If you think thre's no ambiguity with what is meant by $\dim(X)$ when $X$ is a square matrix, then one can note that $MM^T$ is $m\times m$ and $M^TM$ is $n\times n$, so that $\dim(MM^T)=m$ and $\dim(M^TM)=n$.
