Linear Algebra, Third Edition: Algorithms, Applications, and Techniques

✍ Scribed by Richard Bronson, Gabriel B. Costa, John T. Saccoman

• Publisher: Academic Press/Elsevier
• Year: 2013
• Tongue: English
• Leaves: 532
• Edition: 3
• Category: Library

✦ Synopsis

Key Features
Introduces deductive reasoning and helps the reader develop a facility with mathematical proofs
Provides a balanced approach to computation and theory by offering computational algorithms for finding eigenvalues and eigenvectors
Offers excellent exercise sets, ranging from drill to theoretical/challeging along with useful and interesting applications not found in other introductory linear algebra texts

In this appealing and well-written text, Richard Bronson starts with the concrete and computational, and leads the reader to a choice of major applications. 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 and 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.

Prerequisite: One year of calculus is recommended.

Readership: Sophomore- and junior- level students in introductory linear algebra

✦ Table of Contents

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