Definition:Irreducible Logical Matrix

Definition

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

$\mathbf A$ is irreducible if and only if:

$\forall i, j \in \closedint 1 k : \exists n \in \Z_{>0}$: element $\tuple {i, j}$ of $\mathbf A^n$ is strictly positive

where $\mathbf A^n$ denotes the $n$th power of $\mathbf A$.

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