Linear Algebra Done Right

Fourth edition covering Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues. Takes a developmental approach emphasizing motivation and examples.

Jim Hefferon

Covers systems of linear equations, vectors, matrices, vector spaces, determinants, eigenvalues, and linear transformations. Includes a GNU Free Documentation License appendix.

Robert A. Beezer

Covers systems of equations, matrices, determinants, spectral theory, vector spaces, and linear transformations. Includes sections on polar and spherical coordinates.

Ken Kuttler

Honors course lecture notes covering vector spaces, linear transformations, eigenvalues, and least squares regression. Written in an informal, accessible style with exercises throughout.

David Lerner

Companion notes for the Coursera course on matrix algebra. Covers matrices, systems of linear equations, vector spaces, eigenvalues, and matrix exponential with practice problems and solutions.

Jeffrey R. Chasnov