Linear Algebra
3rd Edition
Algorithms, Applications, and Techniques
Description
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.
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
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
Details
- No. of pages:
- 536
- Language:
- English
- Copyright:
- © Academic Press 2014
- Published:
- 25th October 2013
- Imprint:
- Academic Press
- Paperback ISBN:
- 9780123914200
- eBook ISBN:
- 9780123978110
About the Author
Richard Bronson
Fairleigh Dickinson University, NJ, USA
Affiliations and Expertise
Fairleigh Dickinson University, NJ, USA
Gabriel B. Costa
Father Gabriel B. Costa, Ph.D. Department of Mathematical Sciences United States Military Academy West Point, NY
Affiliations and Expertise
United States Military Academy at West Point, NY, USA
John T. Saccoman
Affiliations and Expertise
Seton Hall University
Reviews
“…presents linear algebra in an accessible and rigorous manner…This is a well-organized textbook that intends to aid a student as much as possible. It strikes me as an excellent book for a first linear algebra course that students would likely also find useful as a reference as they advance through the mathematics curriculum.”--MMA.org, July 09, 2014
"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…Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward…The book also includes ample exercises with answers and hints."--Zentralblatt MATH, 1278.15001
"The quality of the exercises is better than that of Anton. Bronson's exercises seem more original and less trivial. While he does have routine drill problems his non-routine problems require the student to either extend the student's knowledge base or fill in a portion of a proof."--Renee Britt, Louisiana State University
"I appreciate the slow increase in the progression of difficulty with proofs... I regard the exposition as superior. Prof. Bronson's text is the best example I've ever seen of motivating definitions in linear algebra, right from the very first page... Bronson incorporates the application first, thus motivating the definition, going from concrete to abstract, instead of the reverse."--Michael Ecker, The Pennsylvania State University