Linear Algebra

MIT's 18.06SC is the OpenCourseWare Scholar edition of Gilbert Strang's linear algebra course, recorded in fall 2011 and organised so that an independent learner can work through it without a classroom. The material is split into three units. Unit I covers Ax = b and the four fundamental subspaces: the geometry of linear equations, elimination, LU factorization, vector spaces, column space and nullspace, independence, basis and dimension. Unit II moves to least squares, determinants and eigenvalues, including projections, Gram-Schmidt, Cramer's rule, diagonalization, differential equations, Markov matrices and Fourier series.

Unit III treats positive definite matrices and applications such as the fast Fourier transform, Jordan form, the singular value decomposition, linear transformations and the pseudoinverse. Each session pairs a full lecture video with summary notes, suggested readings in Strang's textbook, a problem-solving video by a recitation instructor, and problem sets with solutions; three exams and a final, all with solutions, are included, along with instructor insights. Everything is free to view and download under the OpenCourseWare Creative Commons licence, there is no account to create, and no certificate is offered. The same course is also mirrored in MIT's Open Learning Library, where you can enter answers and get instant feedback.