Definition:Period of Logical Matrix

Definition

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

The period of $\mathbf A$ is defined as:

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

where $\gcd$ denotes the greatest common divisor.

Sources

• 1990: William Parry and Mark Pollicott: Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics: Chapter $1$: Subshifts of Finite Type and Function Spaces