The first edition of this book was published in 1980. Many significant changes were made for the second edition (1986), most notably the exercise sets were greatly expanded and the linear transformations chapter of the book was completely revised. Each of the following editions has seen significant modifications including the addition of comprehensive sets of MATLAB computer exercises, a dramatic increase in the number of applications, and many revisions in the various sections of the book. I have been fortunate to have had outstanding reviewers and their suggestions have led to many important improvements in the book. For the ninth edition we have given special attention to Chapter 7 as it is the only chapter that has not seen major revisions in any of the previous editions. The following is an outline of the most significant revisions that were made for the ninth edition.