Let \({A_1,...,A_k}\) be a finite set of matrices. We define a pressure function \(p(t) \)by \(\lim_{n\to\infty} (1/n) \log  \sum_{W\in [k]^n} \|A_W\|^t \)and the associated matrix equilibrium states (measures on \([k]^Z\)). We study a simple example of this type, identifying an explicit phase transition and giving a qualitative description of the equilibrium states for all real \(t\).  (joint work with Dylan Bansard-Tresse and Reza Mohammadpour).