Linear Algebra

Linear Algebra

Algorithms, Applications, and Techniques

2nd Edition - March 5, 2007

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  • Authors: Richard Bronson, Gabriel Costa
  • eBook ISBN: 9780080510262

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Description

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.

Key Features

  • Introduces deductive reasoning and helps the reader develop a facility with mathematical proofs
  • Gives computational algorithms for finding eigenvalues and eigenvectors
  • Provides a balanced approach to computation and theory
  • Superb motivation and writing
  • Excellent exercise sets, ranging from drill to theoretical/challeging
  • Useful and interesting applications not found in other introductory linear algebra texts

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

Product details

  • No. of pages: 520
  • Language: English
  • Copyright: © Academic Press 2007
  • Published: March 5, 2007
  • Imprint: Academic Press
  • eBook ISBN: 9780080510262

About the Authors

Richard Bronson

Richard Bronson has written several books and numerous articles on Mathematics. He has served as Interim Provost of the Metropolitan Campus, and has been Acting Dean of the College of Science and Engineering at the university in New Jersey.

Affiliations and Expertise

Professor of Mathematics and Computer Science, Fairleigh Dickinson University; Senior Executive Assistant to the President

Gabriel Costa

Gabriel B. Costa is currently a visiting professor at the United States Military Academy at West Point and is on the faculty at Seton Hall. He is a priest and a mathematician and holds many titles which he fills with distinction. He has a B.S., M.S. and Ph.D. in Mathematics from Stevens Institute of Technology. He pioneered one of the first courses in Sabermetrics at West Point, and he has also co-authored two other Academic Press books with Richard Bronson, Matrix Methods, Third Edition, as well as with John T. Saccoman, Linear Algebra: Algorithms, Applications, and Techniques, Third Edition.

Affiliations and Expertise

Department of Mathematical Sciences, United States Military Academy, West Point, NY, USA

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