The Garden of Eden theorem for linear cellular automata
Tullio G. Ceccherini-Silberstein, Michel Coornaert · Ergodic Theory and Dynamical Systems · 2006
Let V be a finite-dimensional vector space over a field ${\mathbb{K}}$ and let G be a countable amenable group. Let $\tau \colon V^G \to V^G$ be a linear cellular automaton. We prove that $\tau$ is surjective if and only if it is pre-injective.