Foundations for Machine Learning

Currently Playing: Foundations for ML | Linear Algebra | Product of 2 matrices = Composite Transformation [Lecture 5]

Mathematical Foundations for Machine Learning Linear Algebra is one of the foundational pillars of Machine Learning. Why? Because Machine Learning relies heavily on linear transformations. When you multiply a vector by a matrix, you’re performing a linear transformation, changing one vector into another. This is exactly what matrix multiplication accomplishes. But there’s more! When we multiply two matrices together, the result is a composite linear transformation—meaning the effect of two transformations can be combined into a single operation. This concept not only helps us understand complex transformations in ML but also gives an intuitive path to proving the associative property of matrix multiplication. In my new lecture titled Foundations for Machine Learning | Linear Algebra | Product of 2 matrices = Composite Transformation, I introduce the idea of linear transformations in ML and explain the power of combining them. By tracking how unit vectors 𝑖 and𝑗 are affected, we develop an intuition for defining transformations through matrices and, importantly, how these transformations interact. For the past 4 months, I’ve been developing this course to provide strong foundations for ML, available on Vizuara’s YouTube channel under Foundations for Machine Learning. This 45-hour course contains around 65 lectures and requires no prerequisites—just a logical mindset and a commitment to consistent learning. I’ve simplified the content as much as possible, focusing on geometric and logical intuition rather than purely mathematical steps. Check out this lecture here; I’m sure you’ll enjoy it: https://youtu.be/wBW1Y8NCc9s