  We establish a matrix generalization of the ultradiscrete fourth Painlev\'e
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.
