Linear Algebra: Theory and Applications, 2nd Edition

CHAPTER TWOVector Spaces

2.1 EUCLIDEAN VECTOR SPACES

I hear and I forget. I see and I remember. I do and I understand.

CHINESE PROVERB

Mathematics is not a spectator sport.

—ANONYMOUS

At a later point in this book, we shall consider and see many examples of the abstract concept of a vector space. Here, however, we introduce an important example of a vector space—one that can serve as a model for all the others! In addition, we discuss applications involving electrical networks subject to Ohm’s law and Kirchhoff’s laws, or other types of networks such as traffic grids.

n-Tuples and Vectors

First, let us review some terminology from previous discussions, especially Section 1.2. We fix a positive integer n. An n-tuple of real numbers is a list of ...