Boolean Matrix

Topics: Discrete Mathematics

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A boolean matrix is a matrix such that $a_{ij}=0$ or $a_{ij}=1$ $\forall i,j\in \mathbb{N}$.

Given $m,n\in \mathbb{N}$, the notation for a boolean matrix $A$ is:

$$A=\left(\begin{array}{ccc}{a}_{11}& \dots & a_{1n}\\ ⋮& & ⋮\\ a_{m1}& \dots & a_{mn}\end{array}\right)\in \{0,1{\}}^{m\times n}$$

We represent the set of $m\times n$ boolean matrices with $\{0,1{\}}^{m\times n}$.

Diagonal Matrix

Note that if $a_{ij}=0$ for $i\ne j$, then the matrix is diagonal.