# Linear Algebra with Applications

W. Keith Nicholson, University of Calgary

Copyright Year: 2018

Last Update: 2021

Publisher: Lyryx

Language: English

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

The book covers all main areas and ideas in any regular Linear Algebra course such as: Determinants, Vector Spaces, Eigenvalues, etc. It does a great job in showing real life applications of the concepts presented throughout the book. read more

The book covers all main areas and ideas in any regular Linear Algebra course such as: Determinants, Vector Spaces, Eigenvalues, etc. It does a great job in showing real life applications of the concepts presented throughout the book.

After reading several chapters in the book, I have not found any errors, typos, etc. They did a great job proof reading the material before publishing it.

The text content is actual. The book makes reference to companies like Google, Computer design, etc. when presenting their ideas and applications. The wrote them in such a way that it will be very easy in the future to update their content.

The text contains several paragraphs inside every section where they explain in every day English how the ideas presented are used in real life. They have done an excellent job using LaTeX. The graphs presented are of a superb quality. It is very easy to notice that the author took the extra time to make sure everything was presented in a very professional way.

The text is self-consistent on its entirety. The notation, font type, etc. remains the same from section to section.

The text clearly shows with headings and colors where sections, homework, applications, etc. are presented. The way it is organized makes it very easy to read for instructors and students alike.

The topics are presented in the logical way any Linear Algebra course is typically presented. They have been very thoughtful about including a couple of introductory chapters before presenting the general idea of a Vector Space. This is of great help for students trying to understand the common properties behind every single Vector Space in Mathematics.

The pdf shows no navigation problems when opening it in different browsers like Google Chrome, Safari and Internet Explorer. All book elements such as text, graphs, headings,... look extremely clear and neat.

I have not found any grammatical errors after reading most of the pdf. The wording use is clear, consistent and to the point.

I have not found any content that could be insensitivity or offensive to any culture. I have not found any references to race, sex or religion.

The author made a SUPERB job when creating this text. Explanations are very clear. There are plenty of examples for the students to reference to. The homework assignment problems cover a wide variety of difficulty levels, from the most basic to the most advance. Above all, I have really liked the amount of real life applications presented in pretty much every single chapter of the book.

The text covers topics in our syllabus. read more

The text covers topics in our syllabus.

I did not find any error reading it.

The application sections are good.

The text was easy to read.

The text is consistent in terminology.

The text is easily divided into small sections.

The order of the topics made sense to me.

I did not experience any issues with the interface.

I did not find grammatical errors.

It is not culturally insensitive.

I plan on using this for my course next semester.

## 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

## Ancillary Material

## About the Book

After being traditionally published for many years, this formidable text by W. Keith Nicholson is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today's students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning.

Overall, 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).

## 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.