A First Course in Linear Algebra

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

Jim Hefferon

A novel approach to linear algebra that avoids determinants until the end. Covers vector spaces, finite-dimensional spaces, linear maps, polynomials, eigenvalues, inner product spaces, and operators.

Sheldon Axler

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

Robert A. Beezer

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