Functional Models in Linear Algebra

This paper examines the role of functional models in linear algebra and some related areas of application, notably linear systems theory. This approach adopts an intermediate level of abstraction, somewhere between abstract module theory on the one hand and matrix theory on the other. It is a powerful method which simplifies many proofs, provides insights, and illuminates the less obvious connections between linear algebra and operator theory, approximation theory, moment problems, interpolation, and control theory. 1