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This paper extends the theory of autonomous linear machines (LMs). The theory of the extension field has provided the foundation for the design of such machines referred to as Extended Linear Machines (ELM). An analytical framework has been reported to completely characterize the vector subspace generated by an ELM and also different variations of LMs having cyclic, as well as noncyclic vector subspaces. This formulation has resulted in a single algorithm that characterizes each of the vector subspaces in terms of cyclic and noncyclic subspaces. An ELM significantly reduces the computation time for characterizing the model and study of the behavior of the physical system compared to conventional binary linear machines.