Term for set of all possible $n \times n$ zero-one matrices for a given $n$? Is there a term in mathematics for the SET of all possible $n \times n$ zero-one matrices?
In other words, for a particular $n \in \mathbb{Z}^+$, is there a term for the set of all possible $M=[m_{ij}]$ such that either $m_{ij}=0$ or $m_{ij}=1$ for $1\le i \le n$ and $1\le j \le n$?
$\{ M=[m_{ij}] : m_{ij}=1 \vee m_{ij}=0, 1\le i \le n, 1\le j \le n\}$
Thank you.
 A: I would call such a matrix an adjacency matrix since basically that would be choosing to represent the relation as a graph with vertices in $S$. (This was more relevant before the OP removed the original context.)
These are sometimes collectively called (even with dimensions $m,n$) binary matrices.
There is a slight conundrum with what the entries actually are. You might or might not operate with binary arithmetic or binary operations on the entries. For an adjacency matrix, you often want the entries to be positive integers with their operations.  This allows you to compute $n$-th order adjacency in a graph.
But in your case, you're looking for simply a true/false that an element is in the relation: then maybe it is reasonable to think of them as elements in the field of two elements.  I'm not sure what algebraic interpretation could be attached to operations with these matrices, though.
A: It is the set ${\Bbb B}^{n \times n}$ of $n \times n$ Boolean matrices. You can extend the notation to ${\Bbb B}^{n \times m}$, the set of $n \times m$-matrices with entries in the Boolean semiring.
