The term "UMIST linear system" is not widely recognized in standard literature on linear systems, engineering, or mathematics. However, it seems likely that you could be referring to topics related to linear systems studied or developed at the University of Manchester Institute of Science and Technology (UMIST), which was a higher education institution in the UK that specialized in engineering, science, and technology. In general, a linear system refers to a mathematical model or physical system that can be described by linear equations.
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