|
Date |
Topic |
Book |
HomeworkHmwk |
Practice ProblemsProbs |
Jan. |
10 |
Introduction to determinants |
|
|
|
|
12 |
Axiomatic characterization of the determinant |
|
|
|
|
13 |
Bilinearity and determinants in ℝ2 |
|
|
|
|
17 |
Trilinearity and determinants in ℝ3 |
§4.2 |
|
|
|
19 |
The determinant in any dimension |
§4.2 |
|
|
|
20 |
Permutations and the determinant formula |
§4.2 |
H13 |
|
|
24 |
Calculating the determinant |
§4.2 |
A13 |
1 – 15
|
|
26 |
More determinant calculations |
§4.2 |
|
16 – 20, 22, 23, 26 – 29
|
|
27 |
Cramer's Rule |
§4.2 |
H14 |
35 – 38, 57 – 60
|
|
31 |
The classical adjoint |
§4.2 |
A14 |
61 — 64
|
Feb. |
2 |
Bases and coordinates |
§6.3 |
|
1, 2, 3, 4 (part a only)
|
|
3 |
Change of basis |
§6.3 |
H15 |
1, 2, 3, 4 (parts b, c, d, e)
|
Feb. |
7 |
Change of basis II |
|
A15 |
|
|
9 |
In-class exam #3 |
|
|
|
|
10 |
Iterating linear transformations |
§3.7 |
H16 |
5 – 8, 10
|
|
14 |
Eigenvalues and Eigenvectors |
§4.3 |
A16 |
§4.1: 13–17
|
|
16 |
Finding Eigenvalues and Eigenvectors |
§4.3 |
|
1–6 (parts a and b)
|
|
17 |
Diagonalization |
§4.4 |
H17 |
5–7
|
|
21 |
|
|
|
|
|
23 |
Reading Week |
|
|
|
|
24 |
|
|
|
|
|
28 |
Eigenspaces |
§4.3 |
A17 |
1–6 (parts c and d)
|
Mar. |
2 |
More Diagonalization |
§4.4 |
|
8–15, 16–18
|
|
3 |
End of the proof on Diagonalization |
§4.4 |
H18 |
|
|
7 |
Complex Numbers |
App. C |
A18 |
|
|
9 |
Complex Eigenvalues and Eigenvectors |
|
|
|
|
10 |
Dominant Eigenvalues |
§4.5 |
H19 |
9–12
|
|
14 |
The Gerschgorin disk theorem |
§4.5 |
A19 |
47–50
|
|
16 |
In-class exam #4 |
|
|
|
|
17 |
Some Eigenapplications |
§4.6 |
H20 |
7–9
|
|
21 |
Introduction to abstract vector spaces |
§6.1 |
A20 |
5–10
|
|
23 |
Subspaces, bases, coordinates |
§6.1-2 |
|
§6.1: 29, 33, 35, 36
|
|
24 |
Linear transformations |
§6.4 |
H21 |
5, 7, 8, 16
|
|
28 |
Dimension, Rank-nullity theorem |
§6.5 |
A21 |
3, 4, 10, 12
|
|
30 |
Inner product spaces |
§7.1 |
|
1, 2, 5, 9, 10, 11
|
|
31 |
Orthonormal bases |
§5.1 |
H22 |
1–6, 11–15
|
Apr. |
4 |
Gram-Schmidt orthogonalization |
§5.3 |
A22 |
1–6, 11, 12
|
|
6 |
Least-squares solutions |
§7.3 |
|
19, 20, 23, 24
|
|
7 |
Least-squares solutions II |
§7.3 |
H23 |
|
|
11 |
|
|
A23 |
|
|
13 |
|
|
H24 |
|
|
14 |
|
|
A24 |
|