Linear Algebra. Algorithms, Applications, and Techniques

✍ Scribed by Richard Bronson, Gabriel B. Costa and John T. Saccoman (Auth.)

• Publisher: Academic Press
• Year: 2014
• Tongue: English
• Leaves: 519
• Edition: 3
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Content:
Front Matter, Pages i-ii
Copyright, Page iv
Dedication, Page v
Preface, Pages ix-x
About the Authors, Page xi
Chapter 1 - Matrices, Pages 1-91
Chapter 2 - Vector Spaces, Pages 93-173
Chapter 3 - Linear Transformations, Pages 175-235
Chapter 4 - Eigenvalues, Eigenvectors, and Differential Equations, Pages 237-288
Chapter 5 - Applications of Eigenvalues, Pages 289-321
Chapter 6 - Euclidean Inner Product, Pages 323-378
Appendix A - Jordan Canonical Forms, Pages 379-411
Appendix B - Markov Chains, Pages 413-424
Appendix C - More on Spanning Trees of Graphs, Pages 425-431
Appendix D - Technology, Pages 433-434
Appendix E - Mathematical Induction, Page 435
Answers and Hints to Selected Problems, Pages 437-514
Index, Pages 515-519

✦ Subjects

Математика;Линейная алгебра и аналитическая геометрия;Линейная алгебра;