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Matrix equations are omnipresent in (numerical) linear algebra and systems theory. Especially in model order reduction (MOR) they play a key role in many balancing based reduction methods for linear dynamical systems. When these systems arise from spatial discretizations of evolutionary partial differential equations, their coefficient matrices are typically large and sparse. Moreover, the numbers of inputs and outputs of these systems are typically far smaller than the number of spatialarXiv:2003.02088v2 fatcat:tukxcjpyl5bzpbeejxm233opza