Singular Value Decomposition: Theory and Applications

This lecture covers the theory and applications of Singular Value Decomposition (SVD). It explains the concept of SVD, the properties of the decomposed matrices, and the uniqueness of the factorization. The lecture also discusses the approximation of matrices by low-rank matrices, the Eckart-Young theorem, and the minimization of Frobenius norm. Additionally, it explores the reduction of dimensionality using SVD and the interpretation of the decomposed matrices in terms of explaining data variance. The instructor emphasizes the importance of SVD in various fields due to its unique properties and practical applications.