Linear Algebra: An Introduction

In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete and computational, and leads the reader to a choice of major applications (Markov chains, least-squares approximation, and solution of differential equations using Jordan normal form).

The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed features, this text will be a pleasure for professionals, teachers, and students.

. Introduces deductive reasoning and helps the student develop a familiarity with mathematical proofs
. Gives computational algorithms for fi nding Eigenvalues and Eigenvectors
. A balanced approach to computation and theory
. Exercise sets ranging from basic drill to theoretical/challenging
. Useful and interesting applications not found in other introductory linear algebra texts

PREFACE, 1. MATRICES, 2. VECTOR SPACES, 3. LINEAR TRANSFORMATIONS, 4. EIGENVALUES, EIGENVECTORS, AND DIFFERENTIAL EQUATIONS, 5. EUCLIDEAN INNER PRODUCT, APPENDIX A: DETERMINANTS, APPENDIX B: JORDAN CANONICAL FORMS, APPENDIX C: MARKOV CHAINS, APPENDIX D: THE SIMPLEX METHOD, AN EXAMPLE, APPENDIX E: A WORD ON NUMERICAL TECHNIQUES AND TECHNOLOGY, ANSWERS AND HINTS TO SELECTED PROBLEMS, INDEX