Free online courseLinear Algebra for Machine Learning

Course Description

Machine learning becomes far less mysterious when you can read the math it is built on. This free online course helps you develop the linear algebra intuition and practical fluency that power modern AI, from understanding how data is represented to explaining why familiar algorithms behave the way they do.

You will move from the basics of linear systems to the language used in ML libraries: scalars, vectors, matrices, and higher-dimensional tensors. Instead of treating shapes as error messages, you learn to think in dimensions, transposition, indexing, and batch representations that show up in real projects such as images and datasets. Along the way, you practice core operations like dot products, element-wise arithmetic, and reductions, so computations feel predictable and easy to debug.

The course also builds a strong geometric understanding of matrices as transformations. You connect multiplication, identity, symmetry, diagonals, and orthogonality to concrete consequences like efficiency, stability, and what it means to preserve structure. From there, you tackle the ideas that repeatedly surface in machine learning: determinants and invertibility, eigenvectors and eigenvalues, and how decomposition methods reveal what a model can and cannot learn from data.

Finally, you bring it together with tools that are essential for real ML work with non-square, noisy, or overdetermined data: singular value decomposition, the Moore-Penrose pseudoinverse, and least-squares regression. You will also see how concepts like trace and Frobenius norm connect neatly, and why PCA is naturally expressed in linear algebra terms. With frequent questions and exercises to reinforce each step, you finish with a clearer mental model, stronger computational instincts, and a foundation you can immediately apply to machine learning pipelines and interviews.