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The tools, ideas, and insights from linear algebra, abstract algebra, andfunctional analysis can be extremely useful to signal processing and systemtheory in various areas of engineering, science, and social science includingapproximation, optimization, parameter identification, big data, etc. Indeed,many important ideas can be developed from the simple operator equation  A x = b  by considering it in a variety of ways. If x and if b are vectors from thesame or, perhaps, different vector spaces and A is an operator, there are threeinteresting questions that can be asked which provide a setting for a broadstudy.

Vector Space and Matrix Methods in Signal and System Theory