| Jan. 28 |
1.1-1.2, Appendix A, Appendix C (pgs. 1-5, 417-426, 432-444) |
vector space, complex numbers, matrices, systems of linear equations, determinants |
| Jan 31 |
1.3-1.7 (pgs. 5-20) |
subspaces, spans, linear dependence and independence |
| Feb. 4 |
2.1-2.4 |
basis, dimension of a vector space, rank, full rank factorization, linear transformations |
| Feb. 6 |
snow day! |
|
| Feb. 11 |
2.5, 2.6, 3.1 |
change of basis, similarity, equivalence relation, polynomial bases, lagrange interpolation, Cramer's Rule, block matrices |
| Feb. 13 |
3.2, 3.3, 4.1, 4.2 |
direct sums of block partitions, determinants of block matrices, Rank-Nullity Theorem, more on rank |
| Feb. 18 |
4.3, 4.4 |
LU factorization, row equivalence |
| Feb. 20 |
no class |
|
| Feb. 25 |
5.3-5.5 |
inner products, norms, normed vector spaces |
| Feb. 27 |
6.1-6.4 |
orthonormal sequences, orthonormal bases, Gram-Schmidt, Riesz Representation Theorem |
| Mar. 4 |
6.5-6.7, 7.1 |
more on orthonormal bases, adjoints, Parseval's Identity, Bessel's Inequality, unitary matrices |
| Mar. 6 |
7.2-7.5 |
change of basis for orthonormal bases, unitary similarity, permutation matrices, upper Hessenberg matrices |
| Mar. 11 |
7.4, 8.1-8.3 |
QR factorization, orthogonal complement, minimum-norm solution, orthogonal projection |
| Mar. 13 |
8.4-8.6 |
Best Approximation, "solutions" to inconsistent systems, invariant subspaces |
| Mar. 25 |
8.6, Appendix B, 9.1-9.3 |
invariant subspaces, polynomials, eigenvalues and eigenvectors, complex eigenvalues |
| Mar. 27 |
10.1-10.4 |
characteristic polynomial, multiplicities related to similarity and diagonlaization |
| Apr. 2 |
9.5, 11.1-11.3 |
eigenvectors of commuting matricies, Schur's Triangulation Theorem, Cayley-Hamilton Theorem, minimal polynomial |
| Apr. 4 |
11.4-11.6 |
linear matrix equations, commuting matrices and triangulation, eigenvalue adjustments |