As the most widely used text on elementary linear algebra, this book, in its 18th year of publication, has been substantially revised and updated. The most significant changes are in the reorganization to allow for earlier coverage of eigenvalues and eigenvectors. Additionally, there are major improvements in exposition, some new text material, changes and additions to the exercises, plus new supplementary software and computer-oriented course materials. As with previous editions, the aim is to present the fundamentals of linear algebra clearly, with basic ideas studied by means of computational examples and geometrical interpretation wherever possible. The proofs are presented so that they will be understood by beginning students with more difficult proofs placed in optional sections. Answers to all problems are given at the end of the text.