Definition:Period of Logical Matrix

Definition
Let $\mathbf A = \sqbrk a_k$ be a logical matrix.

The period of $\mathbf A$ is
 * $\gcd \set { n\in\Z : b_{i,i}>0 \text{ for } \forall i\in\closedint 1 k \text{, where } \sqbrk b := {\mathbf A}^n }$

where $\gcd$ denotes the greatest common divisor.

Remarks

 * We use the convention $\gcd \emptyset = 1$.