Elementary Linear Algebra

Linear algebra continues to be an important course for a diverse number of students for at least two reasons. First, few subjects can claim to have such widespread applications in other areas of mathematics--multivariable calculus, differential equations, and probability, for example--as well as in physics, biology, chemistry, economics, finance, psychology, sociology, and all fields of engineering. Second, the subject presents the student at the sophomore level with an excellent opportunity to learn how to handle abstract concepts. This book provides an introduction to the basic ideas and computational techniques of linear algebra at the sophomore level. It includes carefully selected applications. The book introduces the student to working with abstract concepts: this includes an introduction to how to read and write proofs. In covering the basic ideas of linear algebra, the abstract ideas are carefully balanced by the considerable emphasis on the geometrical and computational aspects of the subject. This edition continues to provide the optional opportunity to use MATLAB or other software to enhance the practical side of linear algebra. What's New in the Eighth Edition We have been very pleased by the wide acceptance of the first seven editions of this book throughout the 34 years of its life. In preparing this edition, we have carefully considered many suggestions from faculty and students for improving the content and presentation of the material. Although a great many changes have been made to develop this major revision, our objective has remained the same as in the first seven editions:to present the basic ideas of linear algebra an a manner that the student will find understandable.To achieve this objective, the following features have been developed in this edition: Old Chapter 1,Linear Equations and Matrices,has been split into two chapters to improve pedagogy. Matrix multiplication is now covered more carefully in a separate section, Section 1.3. Section 1.6,Matrix Transformations,new to this edition, introduces at a very early stage some geometric applications. Section 1.7,Computer Graphics,has been moved from old Chapter 4 to give an application of matrix transformations. Several sections in old Chapters 1 and 4 have been moved to improve the organization, exposition, and flow of the material. Section 1.8,Correlation Coefficient,new to this edition, gives an application of the dot product to statistics. Section 5.6,Introduction to Homogeneous Coordinates,new to this edition, extends and generalizes earlier work on computer graphics. Section 7.9,Dominant Eigenvalue and Principal Component Analysis,news to this edition, includes several applications of this material. One of the applications discussed here is the way in which the highly successful search engine Google uses the dominant eigenvalue of an enormously large matrix to search the Web. Appendix C,Introduction to Proofs,new to this edition, provides a brief introduction to proofs in mathematics. The geometrical aspects of linear algebra have been greatly enhanced with 55 new figures added to this edition. More exercises at all levels have been added. Eigenvalues are now defined in terms of both real and complex numbers. MATLAB M-files have been upgraded to more modern versions. Key Terms have been added at the end of each section, reflecting the increased emphasis in mathematics on communication skills. A Chapter Review consisting of true/false questions and a quiz has been added to each chapter. EXERCISES The exercises form an integral part of the text. Many of them are numerical in nature, whereas others are of a theoretical type. The theoretical exercises (as well as many numerical ones) call for a verbal solution. In thiKolman, Bernard is the author of 'Elementary Linear Algebra', published 2003 under ISBN 9780130457875 and ISBN 0130457876.