28 Algebra
A First Course in Linear Algebra
Robert A. Beezer (University of Puget Sound)
2021
GNU Free Documentation Licence
An introductory textbook designed for university sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form.
Format: Online, PDF
Suggested for: MATH 270, MATH 271
A First Course in Linear Algebra – 10th Edition-2023-B-D
Ken Kuttler, Brigham Young University
2023
Licence: CC BY
This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra.
All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile.
Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text.
Format: Online and PDF
Suggested for: MATH 270, MATH 271
Fundamentals of Matrix Algebra
Gregory Hartman (Virginia Military Institute)
2011
Licence: CC BY-NC
This text deals with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations.
Format: PDF
Suggested for: MATH 270
Introduction to Complex Numbers
Licence: CC BY
This is an introduction to the mathematics of complex numbers, starting from the very basics of their definitions, up to proving theorems for polynomials. The text covers everything required of most first-year mathematics courses on complex numbers with proofs, where appropriate.
Format: PDF
Suggested for: MATH 366
Linear Algebra
Jim Hefferon (St. Michael’s College)
2020
Licences: GNU Free Documentation License or CC BY-SA 2.5
This text covers the standard material for a US undergraduate first course: linear systems and Gauss’s Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges. Ancillary materials are available at the publisher link.
Formats: PDF and LaTeX
Suggested for: MATH 270, MATH 271
Linear Algebra I: Skills, Concepts and Applications
Gregg Waterman (Oregon Institute of Technology)
2016
Licence: CC BY
Systems of linear equations, Euclidean spaces and victors, matrices and vectors, vector spaces and subspaces, linear transformations.
Format: PDF
Suggested for: MATH 270
Linear Algebra Done Right – Fourth Edition
Sheldon Axler, San Francisco State University
2024
Licence: CC BY-NC
Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added.
The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions.
No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
Format: PDF, Hardcopy
Suggested for: MATH 271
Linear Algebra with Applications 
W. Keith Nicholson (University of Calgary) (Lyryx)
2023
Licence: CC BY-NC-SA
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.
Format: PDF, Hardcopy
Suggested for: MATH 270, MATH 271
Matrix Algebra with Computational Applications
Dirk Colbry (Michigan State University)
2021
Licence: CC BY-NC
Matrix Algebra with Computational Applications is a collection of OER materials designed to introduce students to the use of Linear Algebra to solve real-world problems. These materials were developed specifically for students and instructors working in a “flipped classroom” model that emphasizes hands-on problem-solving activities during class meetings, with students watching lectures and completing readings and assignments outside of the classroom.
Format: Online
Suggested for: MATH 270
Tea Time Linear Algebra Explorations in Mathematics – 2nd Edition
Leon Q. Brin
2022
Licence: CC BY-SA
This creation is an all-purpose open source textbook for linear algebra classes of all ilks. Inside you will find a complete and engaging introduction to linear algebra, making it a perfect primary resource for classroom study. Take a ride through the landscape of linear algebra from basic mechanics through inner product spaces.
Formats: PDF
Suggested for: MATH 270, MATH 271
Vector Spaces First: An Introduction to Linear Algebra (Fourth Edition)
Thierry Giordano, Barry Jessup, and Monica Nevins (University of Ottawa)
2021
Licence: CC BY-NC-SA
Created for a first-year university course, this linear algebra textbook takes an unusual approach: it introduces vector spaces at the outset and deals with linear systems only after a thorough introduction to vector spaces. This approach is based on the authors’ experience over the past 25 years that students often need more time to master vector spaces while traditional textbooks relegate the topic to the end of the course. In this way, these new notions at the heart of linear algebra that are often considered abstract and difficult in an introductory course can then be used in the rest of the course as well as in different contexts.
Formats: PDF and LaTeX (on Github)
