Matrices and Vector Spaces: A brief introduction to linear algebra

W. Goddard with help from E. Melville

Full pdf text (without exercises) is here

  1. Cover | Table of contents
Linear Systems and Matrices
  1. Solving Linear Systems | Exercises
  2. Vectors and Linear Combinations | Exercises
  3. Matrix Operations | Exercises
  4. Determinants | Exercises
Spaces and Bases
  1. Subspaces, Bases, and Dimension | Exercises
  2. The Three Matrix Spaces and Coordinate Systems | Exercises
  3. Vector Spaces and Linear Transforms | Exercises
Applications
  1. Eigenvalues | Exercises
  2. Orthogonality | Exercises
  3. Further Applications (under development)
Slides for the text are here