ABSTRACT
This book deals with two main topics: linear algebra, which is the study of linear functions on vector spaces, and multivariable calculus, which is the study of nonlinear functions on vector spaces. The first step for each is the study of vector spaces, and this is the topic of this chapter. We define vector spaces, subspaces, and linear transformations, and derive some of the in basic properties. We also investigate linear transformations between Euclidean spaces in some detail.
