Definition:Logical Matrix

A logical matrix (or boolean matrix) is a matrix whose entries are all either $$0$$ or $$1$$.

Loop-Digraph
The adjacency matrix for a loop-digraph is a logical matrix:

$$\qquad \begin{pmatrix} 1 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 \\ \end{pmatrix}$$

Relation
A logical matrix can be used as an explicit definition of a binary relation.

The binary relation "is a divisor of" on the set of natural numbers $$\left\{{1, 2, 3, 4}\right\}$$ consists of the set of pairs:


 * $$\left\{{(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 4), (3, 3), (4, 4)}\right\}$$

This relation can be represented by the following logical matrix:


 * $$\begin{pmatrix}

1 & 1 & 1 & 1 \\  0 & 1 & 0 & 1 \\   0 & 0 & 1 & 0 \\   0 & 0 & 0 & 1 \end{pmatrix}$$