ABSTRACT
The purpose of this book is to give a careful development of vector spaces and linear operators, and to show how these abstract concepts are useful in a variety of practical applications. All of the properties discussed and used will be proved, which means that we must choose a starting point-a set of axioms. For our purposes, the starting point will be the axioms of a field. Scalars are intrinsically linked to vectors, and the scalars used must belong to a field.
