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 failures, 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 formal resolution to this problem. This paper presents a formal approach to representing multi-agent coordination, and multi-agent observations, using matrix structures. This representation facilitates easy representation of coordination requirements, modularity, flexibility 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.