Understanding Linear Algebra

David Austin

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Latex source Yes
Exercises Yes
Solutions Yes
License Creative Commons Attribution License

This text is for a first course in linear algebra at the college level that should appeal to students in a variety of majors. It emphasizes the conceptual and geometric foundations of linear algebra with enough depth so that topical applications such as image compression, the page rank algorithm, and principal component analysis can be developed in detail.Throughout the book there are frequent Sage cells designed to help students learn to use computational tools effectively. The book has been in use for a few years at Grand Valley State University, where the author teaches, and has been adopted elsewhere.


  1. Systems of equations
  2. Vectors, matrices, and linear combinations
  3. Invertibility, bases, and coordinate systems
  4. Eigenvalues and eigenvectors
  5. Linear algebra and computing
  6. Orthogonality and least squares
  7. The Spectral Theorem and singular value decomposition