ABSTRACT
In this chapter, we describe some of the mathematics necessary for a good understanding of linear inverse problems and resolution. Further mathematics will be discussed as required in later chapters. The reason for doing this is to make the book reasonably self-contained. The field of linear inverse problems is a superb example of the application of four areas of pure mathematics – linear algebra, functional analysis, probability theory and optimisation theory – to real and commonplace scientific problems. Consequently, a scientist may relate what appear at first sight to be rather abstract mathematical ideas to problems with which he or she is familiar and, in the process, improve their understanding of both their problems and the underlying mathematics.
