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The purpose of this chapter is to give a taste of some of the diversity. Sec¬tion 6.1 introduces the linear algebra in function theory, the broad interaction between linear algebra and analysis, and some of the applications. Section 6.2 examines the singular value decomposition and generalized inverses, an area of pure linear algebra growing out of attempts to deal with numerical difficul¬ties Section 6.3 shows how the equation Ax = b can be solved by iterative methods, an approach often needed when A is very large and sparse. Section 6 4 introduces matrix norms and provides the theory needed for Section 6.3, for defining and understanding condition numbers, and for taking the first step into Banach spaces. Section 6.5 provides an introduction to abstract linear algebra over an arbitrary field. This is the proper context for abstract matrix theory, for the interaction between linear algebra and abstract algebra, and for understanding many applications such as coding theory