**Linear Algebra with Applications** – The aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work.

The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners whereas Chapters 5–9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).

**Contents**show

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## Table of Contents

- 1 Systems of Linear Equations
- 2 Matrix Algebra
- 3 Determinants and Diagonalization
- 4 Vector Geometry
- 5 Vector Space R
- 6 Vector Spaces
- 7 Linear Transformations
- 8 Orthogonality
- 9 Change of Basis
- 10 Inner Product Spaces
- 11 Canonical Forms

A Complex Numbers

B Proofs

C Mathematical Induction

D Polynomials

Selected Exercise Answers

## About the Contributors

### Author

**Dr. W. Keith Nicholson** earned his undergraduate Degree in Applied Mathematics at the University of Alberta, and received his Ph.D. in Pure Mathematics from the University of California at Santa Barbara in 1970. He then moved to the University of Calgary, and has been a professor in the Department of Mathematics and Statistics since 1979, where he has been carrying out research in a branch of algebra called “Ring Theory”. His continuing interest in teaching undergraduate students has led to another book in Linear Algebra (now in its third edition), a text in Abstract Algebra (second edition), and the creation (with Professor Claude Laflamme), of an internet tutorial for Linear Algebra called ILAW (Interactive Linear Algebra on the Web). Keith is married and has two grown sons.