Finite Dimensional Vector Spaces

In this chapter, we define vector spaces to be algebraic structures with operations having properties similar to those of addition and scalar multiplication on Rn. We then establish many important concepts relating to vector spaces, including span, linear independence, bases, dimension, and coordinatization with respect to a basis. Because we are studying vector spaces as a class, this chapter is more abstract than previous chapters. But the advantage of working in this more general setting is that we generate theorems that apply to all vector spaces, not just Rn.