Seismic vulnerability of urban regions depends on the infrastructure systems that need to remain operative during and after earthquakes. In modern societies, the increasing interdependence of the various infrastructures may significantly affect the community resilience because a damage or a failure on a system may propagate to other interconnected ones. In this regard, the original concept of seismic resilience needs to be expanded to a more general definition that may consider the dependence of multiple infrastructures. In particular, this paper aims to develop a formulation of the seismic resilience by proposing an algebraic matrix form for the calculation of the seismic resilience. The presented formulation has the main advantages to be easily implemented in numerical platforms and to calculate the degree of interdependency between infrastructure.