Foundations for Machine Learning

Currently Playing: Foundations for Machine Learning | Linear Algebra | 3D linear transformation [Lecture 4]

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, particularly in three-dimensional space. When you multiply a vector by a matrix, you're performing a linear transformation, changing one vector into another in 3D space. This is exactly what matrix multiplication accomplishes, and visualizing these transformations in three dimensions provides powerful insights into how machine learning algorithms manipulate data. 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. In 3D space, this becomes even more fascinating as we can observe how these transformations affect volumes, planes, and lines. 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 | 3D Linear Transformations", I introduce the idea of linear transformations in three-dimensional space and explain the power of combining them. By tracking how unit vectors 𝑖, 𝑗, and 𝑘 are affected in 3D space, we develop an intuition for defining transformations through matrices and, importantly, how these transformations interact in three dimensions. 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 in three-dimensional space rather than purely mathematical steps. Check out this lecture on 3D linear transformations; I'm sure you'll enjoy seeing these concepts come to life in three dimensions: https://youtu.be/11GtIkzbGwo