This is an early, incomplete draft of a linear algebra textbook. Please see http://projectivepress.com/LinearAlgebra for further information, and a hyperlinked downloadable copy cropped for viewing... More > on-screen.< Less

Linear Algebra by Jim Hefferon is released under the GNU Free Documentation license. Electronic copies may be downloaded for free. Hardcover copies are available for the cost of manufacturing (the... More > publisher receives no additional revenue). The book covers the material of a first undergraduate Linear Algebra course. The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Prerequisites: a semester of calculus. Students with three semesters of calculus can skip a few sections. The approach is developmental. It does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class.< Less

Linear Algebra by Jim Hefferon is released under the GNU Free Documentation license. Electronic copies may be downloaded for free. Hardcover copies are available for the cost of manufacturing (the... More > publisher receives no additional revenue). The book covers the material of a first undergraduate Linear Algebra course. The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Prerequisites: a semester of calculus. Students with three semesters of calculus can skip a few sections. The approach is developmental. It does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class.< Less

This is a book on elementary linear algebra. It is designed for a second year university student who has had beginning courses in math such as calclulus.

It is a first linear algebra course for mathematically advanced students. It is intended for a student who, while not yet very familiar with abstract reasoning, is willing to study more rigorous... More > mathematics that is presented in a "cookbook style" calculus type course. It is also supposed to be a first course introducing a student to rigorous proof and formal definitions.
The target audience explains the specific blend of elementary ideas and concrete examples, which are usually presented in introductory linear algebra texts with more abstract definitions and constructions typical for advanced books.
The book emphasizes topics that are important for analysis, geometry, probability, etc., and does not include some traditional topics. For example, I am only considering vector spaces over the fields of real or complex numbers, since I feel time would be better spent on some more classical topics, which will be required in other disciplines.< Less

(CC BY) This textbook, published by Textbook Equity, is an open education resource released by The Saylor Foundation under a Creative Commons license. The original textbook, written by Kenneth... More > Kuttler, was chosen by the Saylor Foundation, after a thorough peer review, to be the companion textbook to their online course.
This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and speciﬁc algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. However, this is intended to be a ﬁrst course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra.< Less

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader... More > has had calculus. Some optional topics require more analysis than this, however. I think that the subject of linear algebra is likely the most significant topic discussed in undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying so many different topics. Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. This is the point of view of this book, more than a presentation of linear algebra for its own sake. This is why there are numerous applications, some fairly unusual.< Less

Linear algebra is a powerful set of tools for modelling vector quantities and vector transformations. Linear algebra is used in machine learning, computer graphics, chemistry, economics, quantum... More > mechanics, signal processing, etc. Vectors are used all over the place! Linear algebra is the vector-upgrade to your modelling skills. This book contains lessons on linear algebra written in a style that is precise and concise. Each lesson covers one concept at the level required for a university course. The focus of the book is on showing the intricate connections between the abstract concepts of linear algebra, their geometrical interpretation, and the practical computational aspects. This book differs from regular textbooks by the conversational tone it is written in and its focus on intuitive explanations of the procedures of linear algebra. Each concept is illustrated through concrete examples and in connection with applications. The computer algebra system SymPy is used to illustrate tedious computational tasks.< Less

This is a paper-bound edition of a graduate algebra text originally published by Harper & Row as Groups, Rings, Modules, and written by M. Auslander and D. Buchsbaum. I changed the title to... More > conform to the one that Auslander and I had originally preferred.< Less