Logical Matrix/Examples
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Examples of Logical Matrices
Loop-Digraph
The adjacency matrix for a loop-digraph is a logical matrix:
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 ordered 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:
- $\begin {pmatrix}
1 & 1 & 1 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end {pmatrix}$