# Syllabus

We will cover much of parts I through V of
Trefethen and Bau,
along with some supplementary material.

## Some major topics

- Review of basic linear algebra in finite dimensional spaces, including
both R^n and also function spaces.
- Linear independence, bases, norms, matrix factorization, etc.
- Orthogonality and the Singular Value Decomposition (SVD).
- Least squares problems: QR factorizations, Gram-Schmidt, Householder
transformations.
- Conditioning of problems and stability of algorithms.
- Linear systems of equations: Gaussian elimination and LU factorizations.
- The eigenvalue problem: the power method and QR algorithms, relation to SVD.
- Various applications of the above algorithms will also be considered.