2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118223We establish a matrix generalization of the ultradiscrete fourth Painlevé equation (ud-PIV). Well-defined multicomponent systems that permit ultradiscretization are obtained using an approach that relies on a group defined by constraints imposed by the requirement of a consistent evolution of the systems. The ultradiscrete limit of these systems yields coupled multicomponent ultradiscrete systems that generalize ud-PIV. The dynamics, irreducibility, and integrability of the matrix valued ultradiscrete systems are studied.12 pages, 12 figures, Latex2e, Submitted to J. Phys. A, corrections madeExactly Solvable and Integrable SystemsCellular Automata and Lattice Gasestext