Matrix Methods: Singular Value Decomposition

Least-squares approximations of over-determined equations, and least-norm solutions of underdetermined equations. Range and nullspace and their connection to left and right inverses. Symmetric matrices and quadratic forms. Positive definite matrices. Newton's method. Vector Gaussian distributions. Eigenvalues and eigenvectors of symmetric matrices. Matrix norm and the singular-value decomposition. Spectral graph embedding. Low rank approximations. Emphasis on applications from a broad range of disciplines including circuits, signal processing, machine learning, and control systems.