*Matrix Theory and Linear Algebra* is an introduction to
linear algebra for students in the first or second year of
university. The book contains enough material for a 2-semester
course. Major topics of linear algebra are presented in
detail, and many applications are given. Although it is not a
proof-oriented book, proofs of most important theorems are
provided.

1
Systems of linear equations

2
Vectors in ℝⁿ

3
Lines and planes in ℝⁿ

4
Matrices

5
Spans, linear independence, and bases in
ℝⁿ

6
Linear transformations in ℝⁿ

7
Determinants

8
Eigenvalues, eigenvectors, and
diagonalization

9
Vector spaces

10
Linear transformation of vector
spaces

11
Inner product spaces

Appendix A
Complex numbers

- Balancing chemical reactions
- Dimensionless variables
- Resistor networks
- Cryptography: The Hill cipher
- Perspective rendering
- Solving recurrences
- Solving systems of linear differential equations
- Error correcting codes
- Fourier series
- Simplification of quadratic forms
- Principal component analysis

Download the textbook here.

Printed copies of this textbook can be purchased inexpensively from Lulu.com:

- Matrix Theory and Linear Algebra (black and white), CAD $26.00.
- Matrix Theory and Linear Algebra (color), CAD $40.00.

You can get an additional discount by searching the internet for Lulu coupons. You can often find coupons for a 10-15% discount or for free shipping. Hint: the free shipping is often the better deal.

*Matrix Theory and Linear Algebra* is an open text,
licensed under
the Creative
Commons CC BY 4.0 License. This means that it can be
freely downloaded, printed, and shared (subject to some
conditions that are spelled out in the license). The license
also permits making changes. This is ideal for instructors
who would like to add their own material, change notations, or
add more examples or exercises. Please see
the License
for details. If you make revisions, please send them to me so
that I can consider incorporating them in future versions of
this book.

Since this is an open text, typos can be easily fixed and an updated version posted online. It is my intention to fix all typos. If you find a typo (no matter how small), please report it to selinger@mathstat.dal.ca.

Chapter 11.4 (Fourier series): Watch this video for a demonstration of what the functions fromExamples 11.44–46 sound like as audio signals.Chapter 11.12 (Principal component analysis): Here is the senate voting data used in the textbook.

We have developed online homework assignments for this textbook using the MAA's WeBWorK system. We have also developed a set of tutorial worksheets with additional applications. To get these resources, instructors should contact selinger@mathstat.dal.ca.

The LaTeX sources for this textbook are maintained as a GIT repository and can be found at https://github.com/selinger/linear-algebra.

*Matrix Theory and Linear Algebra* in its current form
was adapted, thoroughly revised, and extended by Peter
Selinger for use at Dalhousie University. It is based on the
earlier open text
"A
first course in linear algebra" by Lyryx Learning, which
was in turns an adaptation of the open text
"Elementary
linear algebra" by Ken Kuttler. Please see inside the book
for the full revision history.

Contributors include: Ken Kuttler, Ilijas Farah, Marie-Andrée B. Langlois, Peter Selinger, and the Lyryx Learning Team: Bruce Bauslaugh, Peter Chow, Nathan Friess, Stephanie Keyowski, Claude Laflamme, Martha Laflamme, Jennifer MacKenzie, Tamsyn Murnaghan, Bogdan Sava, Larissa Stone, Ryan Yee, and Ehsun Zahedi. Cover photography by Pok Rie.