Singularity confinement for matrix discrete Painlevé equations

We study the analytic properties of a matrix discrete system introduced by Cassatella and Mañas (2012 Stud. Appl. Math. 128 252–74). The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters except possibly for algebraic subvarieties. This paves the way to a generalization of Painlevé analysis to discrete matrix models. (paper)