In this chapter we will deal with the elements of matrix algebra which we will use throughout the rest of this book. The material presented here is selfcontained. However, the student who has little prior knowledge of most of the topics in this chapter may find it helpful to refer to some of the books indicated at the end in our “For Further Reading” list. In classical mechanics we will be mainly dealing with vectors (and matrices) whose elements will be real. Hence unless explicitly stated, we shall deal in this book with real vectors and real matrices, as opposed to vectors and matrices whose elements may be complex numbers.

The chapter is divided into two main sections. The first is entitled Preliminaries, the second is called Generalized Inverse of a Matrix. We recommend that the reader begin by going to the second section after skimming over the two subsections that precede it. The details will become clearer as greater familiarity with the topics is gained. It is then that (s)he may go back to the section entitled Preliminaries, so that a better groundwork for the chapters to follow will be laid.

Preliminaries

This section contains some of the preliminary material related to vector spaces. The reader is welcome to skip the material here if (s)he is familiar with it. For the beginner, it may be better to simply skim over this section lightly at the first reading.