Week |
Contents |
Week 1 |
Course overview. |
Week 2 |
Review: Diagonalizability of matrices, spectral theorem symmetric matrices, positive square root of positive semidefinite matrices, basics of norms. |
Week 3 |
Matrix norms, induced norms, matrix p-norms, properties of norms, condition number. |
Week 4 |
Sensitivity analysis for linear systems, Scaling and condition number. |
Week 5 |
Back substitution, Gaussinan elimination, LU decomposition, pivoting |
Week 6 | Cholesky decomposition, Plane rotator(Givens rotator), , QR decomposition(Proof using rotators) |
Week 7 | Reflector(Householder transformation), QR decomposition(Proofs using reflectors), Least squares problems. |
Mid semester | 17.02.2020 to 25.02.2020 |