MATH 121B
Course Content: Invariant subspaces, inner product, normal and self-adjoint operators, orthogonal projectors, Jordan canonical form.
Textbooks: Linear Algebra, 4th Edition, S. H. Friedberg, et al., Prentice Hall, 2003.
Prerequisites: Mathematics 3A or 6G; 13.
Location: Lecture in SH 128, MWF 1:00 p.m. - 1:50 p.m.
Discussion Section: Matthew Levy, SSTR 103, TTh 1 p.m. - 1:50 p.m.
Office hours in RH 248: TTh 2:00 p.m. - 4:00 p.m..
My office hours: MWF 2:00 p.m.- 3:00 p.m., or by appointment. Office: RH 440 H.
Exams: There will the midterm exam and a comprehensive final exam as stated below in the Course Schedule. No books are allowed on exams. The dates and times of all exams are fixed so make make sure that you have no conflicting plans. No make up exams will be given under any circumstances. Please remember to bring your student ID to all exams.
Grading: The course grade will be based on homework, midterm and final exams in the following way: homework = 20%, midterm exams = 30% and final exam = 50%.
Curve: The course grade may be curved if the median appears to be far below the B-/C+ region.
Related Links:
Linear Algebra, 4th Edition, S. H. Friedberg, et al., Prentice Hall, 2003.
DAY |
SECTION |
TOPIC |
01. 04/01 M |
5.4 |
Invariant subspaces and Cayley-Hamilton Theorem |
02. 04/03 W |
5.4 |
Complete 5.4 |
03. 04/05 F |
6.1 |
Inner product and norm |
04. 04/08 M |
6.1 |
Complete 6.1 |
05. 04/10 W |
6.2 |
Gram-Schmidt process and orthonormal basis |
06. 04/12 F |
6.2, 6.3 |
Complete 6.2, start 6.3 |
07. 04/15 M |
6.3 |
Adjoint of a linear operator |
08. 04/17 W
|
6.3 |
Complete 6.3 |
09. 04/19 F |
6.4 |
Normal and self-adjoint operator |
10. 04/22 M |
6.4 |
Continue 6.4 |
11. 04/24 W |
6.4, 6.5 |
Complete 6.4, start 6.5 |
12. 04/26 F |
6.5 |
Unitary and Orthogonal operators |
13. 04/29 M |
6.5 |
Complete 6.5 |
14. 05/01 W |
6.6 |
Orthogonal Projections and the Spectral Theorem |
15. 05/03 F |
Review |
|
16. 05/06 M, regular class time |
Midterm |
|
17. 05/08 W |
6.6 |
Complete 6.6 |
18. 05/10 F |
6.8 |
Quadratic forms |
19. 05/13 M |
6.8 |
Complete 6.8 |
20. 05/15 W |
6.11 |
Geometry of orthogonal operators |
21. 05/17 F |
6.11 |
Complete 6.11 |
22. 05/20 M |
7.1 |
Jordan Canonical form I |
23. 05/22 W |
7.1, 7.2 | Complete 7.1, start 7.2 |
24. 05/24 F |
7.2 |
Jordan Canonical form II |
25. 05/29 W |
7.2 |
Complete 7.2 |
26. 05/31 F |
7.3 |
Minimal polynomial |
27. 06/03 M |
7.3 |
Minimal polynomial |
28. 06/05 W |
Review |
|
29. 06/07 F |
Review |
|
| 06/12 Wednesday. 1:30 p.m. -3:30 p.m. | Final Exam |
|
Homework assignments are to be turned in at the beginning of the class. Late homeworks will not be accepted. Only selected problems will be graded.
Homework #1 (due Tuesday 04/09): Sec. 5.4: 1, 2 (b, c, d), 3 (b, c), 6(a, d), 7, 11, 13, 18, 19, 28.
Homework #2 (due Tuesday 04/16): Sec. 6.1: 1, 3, 4(b), 5, 8, 11, 12, 19, 23(a,b,c); Sec. 6.2: 2(b,c).
Homework #3 (due Tuesday 04/23): Sec. 6.2: 1, 2(d, g), 4, 6, 11, 13(c, d), 15(a), 19(a,c); Sec. 6.3: 3(a,c).
Homework #4 (due Tuesday 04/30): Sec. 6.3: 1, 6, 10, 13, 18, 22(b); Sec. 6.4: 1, 2(a, e), 3, 9, 11.
Homework #5 (due Tuesday 05/07): Sec. 6.5: 1, 2(a, b, e), 3, 4, 6, 10, 17, 21.
Homework #6 (due Tuesday 05/14): Sec. 6.6: 1, 2, 3 (do only for the matrices (a), (b), (e) of Exercise 2 Sec. 6.5), 4, 6, 7; Sec. 6.8: 5.
Homework #7 (due Tuesday 05/21): Sec. 6.8: 1, 6, 13, 14, 15, 16, 17(a,c), 24.
Homework #8 (Tuesday due 06/04): Sec. 7.1: 1, 2(a), 3(b), 7(a,b,c,d,e); Sec. 7.2: 3(a,c,d,e), 4(a), 13, 18, 19(a,b).