Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

18.065 is Gilbert Strang's spring 2018 course on the linear algebra behind data analysis, signal processing and machine learning, published on OpenCourseWare with a complete set of video lectures. Its premise is that linear algebra concepts are key to understanding and creating machine learning algorithms, especially deep learning and neural networks, so the course reviews linear algebra with applications to probability, statistics and optimisation, and builds up to a full explanation of deep learning. The lecture sequence starts with the column space, multiplying and factoring matrices, orthonormal columns, eigenvalues and eigenvectors, positive definite and semidefinite matrices, and the singular value decomposition with the Eckart-Young theorem on the closest low-rank matrix. It continues with norms, four ways to solve least squares, difficulties with Ax = b, computing eigenvalues and singular values, randomised matrix multiplication, low-rank updates, derivatives of matrices, and saddle points.

Later lectures cover minimisation step by step, gradient descent and acceleration with momentum, linear programming and two-person games, and stochastic gradient descent, on the way to neural networks. The site also offers readings, problem sets, a final project description, related resources, instructor insights and podcasts. All content is free under a Creative Commons licence, with no account and no certificate.