# How to name a matrix with restricted input values?

How should I refer to a matrix with a restricted domain of possible values that can be stored inside?

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Let's say you want your matrices to have its entries in a subset $X$ of $R$, where $(R, +, \cdot)$ is a ring, (if you're not familiar with the concept of ring, just think of it as a set with a sum $+$ and a multiplication $\cdot$, like the integers $\Bbb Z$).
Then you can denote the set of all matrices which entries are in $X$ as $\mathcal M(X)$. If you want to specify the size of the matrices you can denote it by $\mathcal M_{m\times n}(X)$, for some $m, n\in \Bbb N$.
Now to state that the entries $[m_{ij}]$ of a certain matrix $M$ respect some condition, you just let $X$ be the set of elements of $R$ that respect that condition and say $M\in \mathcal M(X)$.