Eigenvalue Problems: Methods and Applications

This lecture covers the basics of eigenvalue problems, including eigenvalue decomposition, normal and hermitian matrices, iterative methods such as the power method and inverse power method, Gershgorin circles theorem, Rayleigh quotient method, and numerical solutions for quantum particles in arbitrary potentials. It also discusses the application of iterative methods in computational physics, convergence properties, and examples of solving eigenvalue problems in connectivity networks and Google PageRank(TM) matrix.