The author of this free online linear algebra textbook, Robert A. Beezer, has taught linear algebra 39 times (as of May 2014) and has been teaching undergraduate mathematics courses since 1978. He is currently a member of the faculty at the University of Puget Sound.

Beezer lists courses in differential and integral calculus and perhaps some multivariate calculus as prerequisites but reassures students that calculus knowledge is not truly required to be successful with his text. He explains that students will need a “level of mathematical maturity” gained from those courses moreso than actual knowledge of calculus.

Most of the exercises have complete solutions. Those which do not are identified clearly within the text. Beezer encourages students to not peek at the answers too soon and instead try to work the exercises diligently to better master the material.

The text is offered as an online text and a downloadable PDF. However, according to Beezer, the online version is the most complete.

## Table of Contents for *A First Course on Linear Algebra* Online Textbook

- Systems of Linear Equations
- What is Linear Algebra?
- Solving Systems of Linear Equations
- Reduced Row-Echelon Form
- Types of Solution Sets
- Homogeneous Systems of Equations
- Nonsingular Matrices
- Vectors
- Vector Operations
- Linear Combinations
- Spanning Sets
- Linear Independence
- Linear Dependence and Spans
- Orthogonality
- Matrices
- Matrix Operations
- Matrix Multiplication
- Matrix Inverses and Systems of Linear Equations
- Matrix Inverses and Nonsingular Matrices
- Column and Row Spaces
- Four Subsets
- Determinants
- Determinant of a Matrix
- Properties of Determinants of Matrices
- Eigenvalues
- Eigenvalues and Eigenvectors
- Properties of Eigenvalues and Eigenvectors
- Similarity and Diagonalization
- Linear Transformations
- Linear Transformations
- Injective Linear Transformations
- Surjective Linear Transformations
- Invertible Linear Transformations
- Representations
- Vector Representations
- Matrix Representations
- Change of Basis
- Orthonormal Diagonalization
- Preliminaries
- Complex Number Operations
- Sets
- Archetypes
- A-Z
- Reference
- Notation
- Definitions
- Theorems
- Diagrams
- Examples
- Sage
- Proof Techniques
- GFDL License

View this Free Online Material at the source:

A First Course on Linear Algebra