I'm writing a technical document and need to describe some mathematics involving the shape of a matrix. I realize that I can write $X_{m\times n}$ and someone can simply see the dimensions. I'm wondering if there is some symbol for a function that, when applied, yields a result like the following?
$$\psi(X_{m\times n})=(m,n)$$
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$\begingroup$Do you mean that your function acts over some space of the $X_{mn}$ matrices (matrices of dimension $m\times n$), and gives as a result a tuple of indices $(m,n)$, which are just the dimensions of the matrix (or any other integers $m,n$)? That is pretty much what one interprets from the equation you wrote. Something like:\begin{eqnarray} f:X_{mn}\to \mathbb{Z}^{2}|f(X_{mn})=(m,n) \end{eqnarray}The way to read it would be something like: the function $f$ that acting over the space of matrices $X$ of dimension $(m,n)$, gives as a result the pair of integers $(m,n)$. Usually, $f$ is just to declare a generic function acting over some domain; you can of course use any other symbol $\psi$ if you want to, as long as your symbol matches the definition above.
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