This is an introductory graduate level course on numerical linear algebra.
Topics to be covered will include:

1. Review of relevant linear algebra
(a) Vector and matrix norms
(b) Orthogonality
(c) Spectral theory of matrices

2. Direct methods for linear systems
(a) Perturbation theory
(b) Gaussian elimination
(c) Stability of Gaussian elimination
(d) Cholesky method
(e) QR factorization method

3. Least square problems
(a) Normal equation method
(b) QR factorization method
(c) Householder algorithm
(d) Conditioning of least square problems
(e) Stability of least square algorithms

4. Iterative methods for linear systems
(a) Jacobi, Gauss-Seidel, and relaxation methods
(b) Steepest descent methods
(c) Conjugate gradient method
(d) variant Krylov subspace methods

5. Nonsymmetric eigenvalue problems
(a) Power method
(b) Inverse iteration
(c) Orthogonal iteration
(d) QR iteration

6. Symmetric eigenvalue problems
(a) Tri-diagonal QR iteration
(b) Rayleigh quotient iteration
(c) Bisection and inverse iteration
(d) Jacobi's method

7. Singular value decomposition
(a) QR iteration
(b) Jacobi's method
(c) Application to rank-deficient least square problems

Continuation of this course to next semester will be on numerical optimization.