Analysis of Numerical Methods I

Matrix Norms and Induced Norms Singular Value Decomposition Moore-Penrose Pseudoinverse Least Squares and Normal Equations QR Factorization Cholesky Factorization and SPD Matrices Eigenvalues, Spectral Radius, and Gershgorin Theorem Rayleigh Quotient Iteration Orthogonal and Unitary Matrices Projectors and Orthogonal Projections Conditioning, Sensitivity, and Perturbation Bounds Rank-One Updates and Sherman-Morrison Formula Gaussian Elimination and Pivoting Iterative Methods for Linear Systems Jacobi and Gauss-Seidel Methods Fixed-Point Iteration Finite Difference Methods Quadrature Rules Determinants and Hadamard's Inequality Low-Rank Approximation Matrix Rank and Fundamental Linear Algebra Linear Programming and Optimization