| May 1 |
1.1, 1.2 |
Brief review of matrix arithmetic |
| May 6 |
1.3, 1.4 |
Brief review of linear transformations, gaussian elimination, and elementary matrices |
| May 8 |
1.5 |
Right, left, and two-sided matrix inverses |
| May 13 |
1.5 |
Right, left, and two-sided matrix inverses |
| May 15 |
1.6 |
LU factorization |
| May 22 |
1.6, 2.1 |
LU factorization (cont.), ill-conditioned systems |
| May 27 |
2.2, 2.3 |
Vector and matrix norms |
| May 29 |
2.3, 2.4 |
Sensitivity and conditioning |
| Jun 1 |
3.1, 3.2 |
Orthogonal complements, projections, Gram–Schmidt algorithm, diagonalization |
| Jun 3 |
3.3 |
Hermitian and unitary matrices |
| Jun 5 |
3.3, 3.4 |
Unitary diagonalization, Schur decomposition |
| Jun 10 |
3.4 |
Spectral theorem, Cayley–Hamilton theorem |
| Jun 12 |
3.5 |
Positive definite matrices, Cholesky factorization |
| Jun 17 |
3.6 |
QR factorization |
| Jun 19 |
1.1–3.5 |
Midterm test |
| Jun 24 |
3.6, 3.7 |
QR factorization, computing eigenvalues |
| Jun 26 |
3.7 |
Computing eigenvalues, Gershgorin circle theorem |
| Jul 3 |
4.1 |
Singular value decomposition |
| Jul 8 |
4.2, 4.3 |
Fundamental subspaces, principal components, pseudoinverses |
| Jul 10 |
4.4, 4.4 |
Pseudoinverses, Jordan canonical form |
| Jul 13 |
4.4, 4.5 |
Jordan canonical form, the matrix exponential |
| Jul 15 |
5.1, 5.2 |
Quadratic forms and their diagonalization |
| Jul 17 |
5.3 |
Rayleigh's principle, min-max theorem |
| Jul 22 |
Notes |
Review |