Practical Linear Algebra, 3rd Edition

Chapter 14

General Linear Spaces

In Sections 4.3 and 9.2, we had a first look at the concept of linear spaces, also called vector spaces, by examining the properties of the spaces of all 2D and 3D vectors. In this chapter, we will provide a framework for linear spaces that are not only of dimension two or three, but of possibly much higher dimension. These spaces tend to be somewhat abstract, but they are a powerful concept in dealing with many real-life problems, such as car crash simulations, weather forecasts, or computer games. The linear space of cubic polynomials over [0, 1] is important for many applications. Figure 14.1 provides an artistic illustration of some of the elements of this linear space. Hence the term “general” in the chapter ...