This textbook is a basic introduction to the ideas and techniques of linear algebra for first- or second-year students who have a working knowledge of high school algebra. Its aim is to achieve a balance among the computational skills, theories, and applications of linear algebra, while keeping the level suitable for beginning students. The contents are arranged to permit enough flexibility to allow the presentation of a traditional introduction to the subject, or to allow a more applied course. Calculus is not a prerequisite; places where it is mentioned are clearly marked and may be omitted.
Linear algebra has wide application to the mathematical and natural sciences, to engineering, to computer science, and (increasingly) to management and the social sciences. As a rule, students of linear algebra learn the subject by studying examples and solving problems. As in the third edition, more than 330 solved examples are included, many of a computational nature, together with a wide variety of exercises. In addition, a number of sections are devoted to applications and to the computational side of the subject. These are optional, but they are included at the end of the relevant chapters (rather than at the end of the book) to encourage students to browse.
The examples also play a role in motivating theorems, although most proofs are included at a level appropriate to the student. This means that the book can be used to give a course emphasizing computation and examples (and omitting many proofs) or to give a more rigorous treatment. Some longer proofs are omitted altogether or are deferred to the end of the chapter.
The fourth edition, like the third, maintains a balance between the abstract theory and matrix computations and applications. It contains two novel features. First, diagonalization is now treated in Chapter 3 (using only determinants and matrix inverses), thereby opening up a wealth of applications early in the book. The second innovation is the introduction of tough concepts such as independence, subspaces, spanning, dimension and linear transformations in Rn in a new "bridging" chapter (Chapter 5). This gives the students a chance to assimilate these ideas before the introduction of abstract vector spaces, and so mitigates the effect of "hitting the wall".
2003 McGraw-Hill Higher Education