.. _syllabus: ============================================================= Syllabus ============================================================= We will cover much of parts I through V of Trefethen and Bau, `Numerical Linear Algebra `_, along with some supplementary material. Some major topics ------------------ * Review of basic linear algebra in finite dimensional spaces, including both :math:`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.