The proposed coordinate/field duality [Phys. Rev. Lett. 78 (1997) 163] is applied to the gauge and matter sectors of gauge theories. In the non-Abelian case, due to indices originated from the internal space, the dual coordinates appear to be matrices. The dimensions and the transformations of the matrix coordinates of gauge and matter sectors are different and are consistent to expectations from lattice gauge theory and the theory of open strings equipped with the Chan-Paton factors. It is argued that in the unbroken symmetry phase, where only proper collections of field components as colorless states are detected, it is logical to assume that the same happens for the dual coordinates, making matrix coordinates the natural candidates to capture the internal dynamics of baryonic confined states. The proposed matrix coordinates happen to be the same appearing in the bound-state of D0-branes of string theory.