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Transition Matrix Theory

In this article we present a unification of the theory of algebraic, singular, topological and directional transition matrices by introducing the (generalized) transition matrix which encompasses each of the previous four. Some transition matrix existence results are presented as well as verification that each of the previous transition matrices are cases of the generalized transition matrix. Furthermore we address how applications of the previous transition matrices to the Conley Index theory carry over to the generalized transition matrix.