Linear Algebra

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

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