Foundations for Machine Learning

Currently Playing: Foundations for ML | Simple intuition of eigenvalues and eigenvectors | Linear Algebra [Lecture 10]

"For Ax=λx, det(A-λI)=0. Sure, but why?" We all know that when Ax = λx, we solve det(A - λI) = 0 for λ to find the eigenvalues. Then we solve (A - λI)x=0 for x to find the eigenvectors. But what exactly are eigenvalues and eigenvectors? Geometrically, why should this condition det(A - λI) = 0 be true for λ being an eigenvalue? This lecture I published on Vizuara's YouTube channel covers a collection of ideas from linear algebra: https://youtu.be/-PmMvHPUto4 You will learn about (not just the math equations, but the actual intuition) 1) Linear transformations 2) Unit vector before and after transformation 3) The geometric intuition behind determinants (very cool stuff) 4) The intuition behind eigenvalues and eigenvectors This lecture is part of the "Foundations for ML course". Learn in detail from my new lecture. My goal is to lay a strong foundation for you in ML: https://youtu.be/-PmMvHPUto4