- Teamwork requires that team members coordinate their actions. The representation of the coordination is a key requirement since it influences the complexity and flexibility of reasoning team-members. One aspect of this requirement is detecting coordination faults as a result of intermittent failures of sensors, communication failures, etc. Detection of such faults, based on observations of the behavior of agents, is of prime importance. Though different solutions have been presented thus far, none has presented a comprehensive and efficient resolution for large-scale teams. This paper presents a formal approach to representing multi-agent coordination, and multi-agent observations, using matrix structures. This representation facil- itates easy representation of coordination requirements, modularity, flexibil- ity and reuse of existing systems. Based on this representation, we present a novel solution for fault-detection that is both generic and efficient for large- scale teams. We demonstrate the modularity of the representation by pre- senting a reuse of existing systems and by importing other models (e.g. hierarchical systems) into the new representation. Finally, we extend the representation to support dynamical aspects of complex systems.