Singular Value Decomposition: Applications and Theorems

This lecture covers the Singular Value Decomposition (SVD) in linear algebra, focusing on its applications and theorems. It explains the concept of SVD, the decomposition into singular values, and the properties of the resulting matrices. The instructor discusses the use of SVD in image processing, matrix rotation, and symmetry. The lecture also delves into the Perron-Frobenius theorem, stability of eigenvectors, and the PageRank algorithm. Additionally, it explores the application of SVD in predicting weather patterns and analyzing transition probabilities in web page popularity. The lecture concludes with practical examples and real-world applications of SVD in various fields.