Definition:Logical Matrix
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Definition
A logical matrix is a matrix whose entries are all either $0$ or $1$.
Also known as
A logical matrix is also known as a boolean matrix, for George Boole.
Examples
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:
- $\begin {pmatrix}
1 & 1 & 1 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end {pmatrix}$
Also see
- Results about logical matrices can be found here.