Linear Algebra : 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.* 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

[Content]

Preface                                            ix
About the Authors                                  xi
    Chapter 1 Matrices                             1  (92)
    Chapter 2 Vector Spaces                        93 (82)
    Chapter 3 Linear Transformations               175(62)
    Chapter 4 Eigenvalues, Eigenvectors, and       237(52)
    Differential Equations
    Chapter 5 Applications of Eigenvalues          289(34)
    Chapter 6 Euclidean Inner Product              323(56)
Appendix A Jordan Canonical Forms                  379(34)
Appendix B Markov Chains                           413(12)
Appendix C More on Spanning Trees of Graphs        425(8)
Appendix D Technology                              433(2)
Appendix E Mathematical Induction                  435(2)
Answers and Hints to Selected Problems             437(78)
Index                                              515