Singular Value Decomposition

This lecture covers the Singular Value Decomposition (SVD) theorem, stating that for a matrix A of rank r, there exist diagonal matrices, U and V orthogonal matrices such that A = UΣV^T. The SVD is not unique, but U and V are. The lecture also discusses the left singular vectors and right singular vectors of A, the proof of SVD, and the normalization process to obtain an orthonormal basis. The lecture concludes with examples demonstrating the SVD theorem in practice.