Definition:Logical Matrix

Definition
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:


 * LoopDigraph.png $\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 $\set {1, 2, 3, 4}$ consists of the set of pairs:


 * $\set {\tuple {1, 1}, \tuple {1, 2}, \tuple {1, 3}, \tuple {1, 4}, \tuple {2, 2}, \tuple {2, 4}, \tuple {3, 3}, \tuple {4, 4} }$

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}$