Linear Algebra II
Instructor: Carl Mautner
Meeting time: MWF 1:10--2 in room Sproul 1340.
Office hours: T 2-3 and F 10-12 (or by appointment) in room 255 Surge
TA: Hyun-Seung Choi
TA Office hours: T 3-5 and Th 1-3 in Pierce Hall 2429.
In this course we will continue from where you left off in Linear Algebra I, by learning more refined properties of linear maps. Our goal will be to understand the structure of linear operators on finite dimensional vector spaces defined over the real and complex numbers. Along the way we will study eigenvalues, minimal polynomials and canonical forms. We will also study inner-product spaces (i.e., vector spaces endowed with extra structure, like the dot product structure on R^n) and the structure of linear operators on them.
I hope to cover the material from Chapters 5-8 of the text.
Linear Algebra Done Right, by Sheldon Axler, 3rd edition. (available free online from UCR computers)
In Math 131 you should have learned the material of the text up to Section 3.D. As this course is a continuation, we will need to build on that material. If some of it is shaky, this will be VERY difficult. In order to succeed in this course, it is essential that you review the material from Math 131.
Grades: The grade will be based on homework assignments (25%), one in-class exam (30%) tentatively set for Friday, February 5, and a final exam (45%) on Wednesday, March 16, 7-10 pm. Final letter grade cut-offs will be made at the end of the quarter and will be no worse the standard scale (e.g., if you get above 90% you are guaranteed an A or A-).
Homework: Homework will generally be assigned each class meeting and due a week later at the beginning of class. A list of the homework problems will be kept on the webpage. Late homework will not be accepted, but the lowest two homework grades will be dropped.
Collaboration: You are encouraged to discuss homework problems with other students. The final write-up of any solution, however, should be your own. Copying other students' solutions is not allowed.
1) M Jan. 4 (Due M Jan. 11) - Start reading pages 132-136 of the book and do exercises 2 and 4 of Section 5.A. Review Chapter 1 and in particular Section 1.C.
2) W Jan. 6 (Due W Jan. 13) - Review Sections 2.A and 3.A and do Exercises 2.A.11 and 3.A.4.
3) F Jan. 8 (Due F Jan. 15) - Review 2.B, 2.C, 3.B and do Exercises 2.B.7 and 3.B.19.
4) M Jan. 11 (will not be collected because of MLK day!) - Review 3.C, do Exercises 3.C.3, 3.C.4 and 3.C.5.
5) W Jan. 13 (Due W Jan. 20) - Review 3.D, Read 5.B, do Exercises 5.A.12, 5.A.21, 5.A.25.
6) F Jan. 15 (Due F Jan. 22) - finish reading 5.B, do Exercises 5.B.3, 5.B.4.
7) W Jan. 20 (Due W Jan. 27) - Start reading 5.C and do the exercises here: pdf.
8) F Jan. 22 (Due F Jan. 29) - Finish reading 5.C and do the exercises here: pdf.
9) M Jan. 25 (Due M Feb. 1) - do the exercises here: pdf.
10) W Jan. 27 (Due W Feb. 3) - Read 6.A and do the exercises here: pdf.
No homework due F Feb. 5 - Midterm study suggestions.
11) W Feb. 10 (Due W Feb. 17) - Read 6.B and do the exercises here: pdf.
12) F Feb. 12 (Due F Feb. 19) - Finish reading 6.B and do the exercises here: pdf.
13) W Feb. 17 (Due W Feb. 24) - Read 6.C and do the exercises here: pdf.
14) F Feb. 19 (Due F Feb. 26) - Finish reading 6.C and do the exercises here: pdf.
15) M Feb. 22 (Due M Feb. 29) - Start reading 7.A and do the exercises here: pdf.
16) W Feb. 24 (Due W Mar. 2) - Read 7.A and do the exercises here: pdf.
17) F Feb. 27 (Due F Mar. 4) - Read 7.B and do the exercises here: pdf.
You can find solutions to the quiz from Feb. 25 here: pdf.
18) M Feb. 29 (Due M Feb. 7) - Read 7.B and do the exercises here: pdf.
You can find solutions to the quiz from Mar. 3 here: pdf.
You can find solutions to the quiz from Mar. 10 here: pdf.