This edition of Elementary Linear Algebra gives an introductory treatment of linear algebra that is suitable for a first undergraduate course. Its aim is to present the fundamentals of linear algebra in the clearest possible way—sound pedagogy is the main consideration. Although calculus is not a prerequisite, there is some optional material that is clearly marked for students with a calculus background. If desired, that material can be omitted without loss of continuity. Technology is not required to use this text, but for instructors who would like to use MATLAB, Mathematica, Maple, or calculators with linear algebra capabilities, we have posted some supporting material that can be accessed at either of the following Web sites: www.howardanton.com www.wiley.com/college/anton Summary of Changes in this Edition This edition is a major revision of its predecessor. In addition to including some new material, some of the old material has been streamlined to ensure that the major topics can all be covered in a standard course. These are the most significant changes: • Vectors in 2-space, 3-space, and n-space Chapters 3 and 4 of the previous edition have been combined into a single chapter. This has enabled us to eliminate some duplicate exposition and to juxtapose concepts in n-space with those in 2-space and 3-space, thereby conveying more clearly how n-space ideas generalize those already familiar to the student. • New Pedagogical Elements Each section now ends with a Concept Review and a Skills mastery that provide the student a convenient reference to the main ideas in that section. • New Exercises Many new exercises have been added, including a set of True/False exercises at the end of most sections. • Earlier Coverage of Eigenvalues and Eigenvectors The chapter on eigenvalues and eigenvectors, which was Chapter 7 in the previous edition, is Chapter 5 in this edition. • Complex Vector Spaces The chapter entitled Complex Vector Spaces in the previous edition has been completely revised. The most important ideas are now covered in Section 5.3 and Section 7.5 in the context of matrix diagonalization. A brief review of complex numbers is included in the Appendix. • Quadratic Forms This material has been extensively rewritten to focus more precisely on the most important ideas. • New Chapter on Numerical Methods In the previous edition an assortment of topics appeared in the last chapter. That chapter has been replaced by a new chapter that focuses exclusively on numerical methods of linear algebra. We achieved this by moving those topics not concerned with numerical methods elsewhere in the text. • Singular-Value Decomposition In recognition of its growing importance, a new section on Singular-Value Decomposition has been added to the chapter on numerical methods. • Internet Search and the Power Method A new section on the Power Method and its application to Internet search engines has been added to the chapter on numerical methods. • Applications There is an expanded version of this text by Howard Anton and Chris Rorres entitled Elementary Linear Algebra: Applications Version, 10th (ISBN 9780470432051), whose purpose is to supplement this version with an extensive body of applications. However, to accommodate instructors who asked us to include some applications in this version of the text, we have done so. These are generally less detailed than those appearing in the Anton/Rorres text and can be omitted without loss of continuity. - Wiley