# Linear Functions and Matrix Theory

• Bill Jacob
Textbook

Part of the Textbooks in Mathematical Sciences book series (TIMS)

1. Front Matter
Pages i-xi
2. Bill Jacob
Pages 1-39
3. Bill Jacob
Pages 40-71
4. Bill Jacob
Pages 72-116
5. Bill Jacob
Pages 117-154
6. Bill Jacob
Pages 155-187
7. Bill Jacob
Pages 188-214
8. Bill Jacob
Pages 215-245
9. Bill Jacob
Pages 246-276
10. Bill Jacob
Pages 277-302
11. Back Matter
Pages 303-330

### Introduction

Courses that study vectors and elementary matrix theory and introduce linear transformations have proliferated greatly in recent years. Most of these courses are taught at the undergraduate level as part of, or adjacent to, the second-year calculus sequence. Although many students will ultimately find the material in these courses more valuable than calculus, they often experience a class that consists mostly of learning to implement a series of computational algorithms. The objective of this text is to bring a different vision to this course, including many of the key elements called for in current mathematics-teaching reform efforts. Three of the main components of this current effort are the following: 1. Mathematical ideas should be introduced in meaningful contexts, with after a clear understanding formal definitions and procedures developed of practical situations has been achieved. 2. Every topic should be treated from different perspectives, including the numerical, geometric, and symbolic viewpoints. 3. The important ideas need to be visited repeatedly throughout the term, with students' understan9ing deepening each time. This text was written with these three objectives in mind. The first two chapters deal with situations requiring linear functions (at times, locally linear functions) or linear ideas in geometry for their understanding. These situations provide the context in which the formal mathematics is developed, and they are returned to with increasing sophistication throughout the text.

### Keywords

Eigenvalue Eigenvector Matrix Matrix Theory algebra linear algebra

#### Authors and affiliations

• Bill Jacob
• 1
1. 1.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-4218-5
• Copyright Information Springer-Verlag New York 1995
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-94451-7
• Online ISBN 978-1-4612-4218-5
• Series Print ISSN 1431-9381
• Buy this book on publisher's site