While exploring the mathematical foundations of machine learning, I discovered Professor Gilbert Strang’s MIT lecture series: Matrix Methods in Data Analysis, Signal Processing, and Machine Learning (18.065).

The course covers the core mathematical tools behind modern data science: matrix factorizations (especially SVD), principal component analysis, optimization methods, neural network fundamentals, and how these concepts power real algorithms. It bridges the gap between pure linear algebra and practical machine learning applications.

The first video completely changed my perspective on linear algebra.

Professor Strang transforms what could be dry, abstract material into something vivid and intuitive. Concepts like basis, eigenvectors, null spaces, and SVD suddenly click into place. You don’t need to master every calculation by hand (though it helps). What matters is visualizing these concepts and knowing when to apply them.

For instance, when Strang explains SVD, you’ll see it’s not just matrix decomposition. You’ll understand how Netflix uses it for recommendations, how it compresses images by keeping only the most important features, and why it’s the backbone of principal component analysis. You start seeing matrices as transformations in space rather than grids of numbers.

After all, computers handle the calculations better than we ever could. As Angus K. Rodgers once said:

Mathematics requires a small dose, not of genius, but of an imaginative freedom which, in a larger dose, would be insanity.

Gilbert Strang’s enthusiasm is contagious. He focuses on building intuition first, then introduces mathematical proofs as logical procedures rather than abstract exercises. This approach makes complex ideas surprisingly accessible.

This course gives you something rare: the ability to truly visualize linear algebra in action. Traditional courses rarely achieve this level of intuitive understanding. If you’re serious about machine learning, this course is worth your time.

One note: you’ll need basic linear algebra knowledge going in. If you’re starting from scratch or need a refresher, check out Strang’s introductory course first: Linear Algebra (18.06).