I recommend this course more often than almost anything else in this catalogue, and it is not an AI course at all. The pattern is consistent enough to be predictable. Someone tells me they are stuck on a deep learning course, that the maths in the backpropagation lecture lost them, that they can implement things but do not understand why any of it works. Almost every time, the actual gap is linear algebra, and almost every time, Strang fixes it.
What makes him remarkable is a refusal to teach mechanically. The standard linear algebra course is a sequence of procedures. Here is Gaussian elimination, here are the steps, here is how to compute a determinant, here is the characteristic polynomial. Students pass by executing the procedures and leave with no idea what any of it means.
Strang goes the other way. He wants you to see that matrix multiplication is a linear combination of columns, that solving a system is asking whether a vector lies in a particular space, that eigenvectors are the directions a transformation does not rotate. The computation follows from the picture rather than replacing it. The organising idea of the course is the four fundamental subspaces, the column space, the null space, the row space and the left null space, and the relationships between them.
Strang returns to this framing again and again until the whole subject hangs off it. Once it lands you have something rare, which is a mental model of an entire field of mathematics that fits in your head at once. Rank, invertibility, least squares, projections, the solvability of a system, all of it becomes a question about which subspace something lives in. For anyone in machine learning the relevance is direct and constant.
Principal component analysis is eigendecomposition of a covariance matrix. Least squares regression is projection onto a column space. Singular value decomposition sits underneath low rank approximation, which is what every parameter efficient fine tuning method is doing. Attention is a sequence of matrix products whose shapes only make sense if you can think in terms of spaces rather than grids of numbers.
People who understand this material read papers differently. The course package on OpenCourseWare is complete. Problem sets, exams, solutions, and in the OCW Scholar version, recitation videos where teaching assistants work through problems, which is the closest thing to supervision that a free course can offer. It is a real course and you can treat it as one.
The limitations are worth stating plainly. The 2010 recordings look like 2010, filmed in a lecture hall with chalk, and if you need production polish you will not get it. Strang is also deliberately informal with proofs. He is teaching engineers and scientists to use linear algebra, not training mathematicians, and a pure mathematics student will find the hand waving uncomfortable.
There is also nothing numerical here, which is a genuine gap for computational work. Nothing on conditioning, nothing on numerical stability, nothing about how these operations actually behave in floating point on a real machine, all of which will bite you eventually. And it is long. Thirty four lectures at fifty minutes each, done properly with the problem sets, is a serious commitment measured in months rather than weekends.
Most people who start it do not finish it, which is a fact about attention rather than about the course. My advice is to do it slowly and alongside something else rather than treating it as a sprint to clear. I have given this 4.8, which is among the highest ratings I hand out, and I am comfortable defending it. It is free, it is complete, it teaches the material that everything else in machine learning is built on, and the teaching is simply better than what most people paid tuition for.
Strang gave his final 18.06 lecture in 2023 after sixty one years at MIT. The recordings will outlast most of what is on this site.