  I revisit a basic question about the noncommutative Yang-Mills theory: if it
exists or not, or more precisely, whether a nonperturbative formulation exists.
As the most promising approach, I consider a formulation based on matrix
models. It is explained that the existence of the noncommutative Yang-Mills
theory is closely related to the Eguchi-Kawai equivalence. I argue that
supersymmetric noncommutative Yang-Mills theory can be defined
straightforwardly. Non-supersymmetric theories, such as QCD and pure bosonic
theories, can presumably be defined, by modifying the ultraviolet and infrared
behaviors appropriately.
