9. Linear Algebra for MLDL: 4 Fundamental Subspaces, Projections & the Basics of Linear Regression

In this lecture, I build the mathematical foundation of Linear Regression starting from core Linear Algebra concepts. We first explore the Four Fundamental Subspaces of a matrix: Column Space Row Space Null Space Left Null Space We then move to orthogonal projections, understanding geometrically and mathematically how a vector is projected onto a subspace. Finally, we connect these ideas to least-squares approximation and Linear Regression, showing why projection is at the heart of finding the best-fitting solution when an exact solution does not exist. The goal is not just to learn formulas, but to understand why Linear Regression works from a Linear Algebra perspective. Topics: Linear Algebra • Four Fundamental Subspaces • Orthogonality • Projections • Least Squares • Linear Regression • Machine Learning Mathematics