Singular Value Decomposition: Applications and Solutions

This lecture covers the Singular Value Decomposition (SVD) of matrices, including the full-form and reduced-form SVD. It explains how SVD provides information about the rank of a matrix, matrix properties, and solutions to linear systems using SVD. The instructor demonstrates solving linear systems with SVD, least squares regression, and matrix pseudoinverse. Additionally, it explores the least squares solution, dyadic expansion, and matrix approximation. The lecture concludes with discussions on fitting linear models, polynomial fits, and weighted least squares regression, emphasizing the importance of minimizing errors and overfitting in data analysis.