This just might be the largest linear algebra textbook ever written. Joel G. Broida and S. Gill Williamson have made their 794-page textbook free for students everywhere. It was written for upper division undergraduate students and graduate students who are studying applied mathematics and pursuing science degrees which require skills in mathematical methods.

The text is divided into three sections and is presented in three separate PDF files. The goal of the authors was to create a comprehensive text that could be used by students and professionals needing a refresher on a particular topic. The proofs are very details to facilitate independent study.

Part of the rationale for such a detailed text is to help students who were exposed to varying techniques and thoughts from earlier courses and instructors. Broida and Williamson mention in their preface that they have found students often find themselves having difficulty with linear algebra because they may have not been exposed to “some trivial mathematical concept” in an earlier class. While this is common in all studies of advanced mathematics, the authors indicate it is ‘particularly acute’ when it comes to linear algebra. With that in mind, they wrote their *Comprehensive Introduction to Linear Algebra* so that it includes the background material necessary to be successful in the course.

## Table of Contents for the *Comprehensive Introduction to Linear Algebra* Online Textbook

- Part I: Basic Linear Algebra
- Chapter 0: Foundations
- Chapter 1: An Introduction to Groups
- Chapter 2: Vector Spaces
- Chapter 3: Linear Equations and Matrices
- Chapter 4: Determinants
- Chapter 5: Linear Transformations and Matrices
- Part II: Polynomials and Canonical Forms
- Chapter 6: Polynomials
- Chapter 7: Linear Transformations and Polynomials
- Chapter 8: Canonical Forms
- Part III: Operators and Tensors
- Chapter 9: Linear Forms
- Chapter 10: Linear Operators
- Chapter 11: Multilinear Mappings and Tensors
- Chapter 12: Hilbert Spaces
- Appendices and Bibliography
- Index

View this Free Online Material at the source:

Comprehensive Introduction to Linear Algebra