We now have a computational toolkit in place and so we can begin our study of linear algebra at a more theoretical level.

Linear algebra is the study of two fundamental objects, vector spaces and linear transformations (see Chapter LT). This chapter will focus on the former. The power of mathematics is often derived from generalizing many different situations into one abstract formulation, and that is exactly what we will be doing throughout this chapter.

Section VS Vector Spaces
Section S Subspaces
Section LISS Linear Independence and Spanning Sets
Section B Bases
Section D Dimension
Section PD Properties of Dimension