Math 115A: Linear Algebra
|
| Date | Topic | Homework |
| 10/2 (Fri) |
Sets and functions |
Prove that the complex numbers
satisfy the axioms of a field. |
| 10/5 (Mon) | Section 1.2: Vector spaces | Please
note that I use the problem numbering from Friedberg,
4th Edition. Section 1.2: 1,4,8,9,10,11,13,16,20 In Problems 13 and 16, if V is a vector space, then verify all the axioms of a vector space. |
| 10/6 (Tues) |
Quiz 1 |
Go to Gradescope to take the quiz between 12:01 am and 11:59 pm Pacific Time on Tues 10/6. The only things you're allowed to use are: the Friedberg textbook, the class notes/videos, and your completed HW. You may not discuss the test with anyone and you may not give or solicit help. Besides the class materials on CCLE, the internet is off limits. Today's a test run, so you're allowed 2 hours from the time you start the quiz. Important: Please handwrite your solutions!!! |
| 10/7 (Wed) | Section 1.3: Subspaces | Section 1.3: 1,6,8,11,15,20,23,24,30 |
| 10/9 (Fri) | Section 1.4: Linear combinations | Section 1.4: 1,2(a)(c)(e),3(a)(c)(e),7,8,13,14 |
| 10/12 |
Section 1.5: Linear dependence/independence | Section 1.5: 1,2(a)(c)(e),4,5,9,15,18 |
| 10/13 (Tues) |
Quiz 2 |
Go to Gradescope to take the quiz between 12:01 am and 11:59 pm Pacific Time. You're allowed 50 minutes from the time you start the quiz - about 30 minutes to do the quiz and another 20 minutes to upload your solutions. Important: Please handwrite your solutions!!! |
| 10/14 |
Section 1.6: Bases and dimension | Section 1.6: 2(a)(c)(e),3(a),6,14,15,17 (We may not get to the definition of dimension until next week; simply take it to be the number of elements of the basis you constructed.) |
| 10/16 |
Section 1.6: Bases and dimension | Section 1.6: 12,20,24,26,28,33,34 |
| 10/19 |
Section 2.1: Linear transformations | Section 2.1: 7,8,9,14(b),15 |
| 10/20 (Tues) |
Quiz 3 |
|
| 10/21 |
Section 2.1: Linear transformations | Section 2.1: 1,2,5,6,17,24,26,28 |
| 10/23 |
Section 2.2: Matrix representation of a linear transformation | Section 2.1: 11,13 Section 2.2: 1,2(a)(c)(f),3,4 |
| 10/26 |
Section 2.2: More on matrix
representations Section 2.3: Composition of linear transformations |
Section 2.2: 5,8,10,11 Section 2.3: 2,3 |
| 10/27 (Tues) |
Quiz 4 |
|
| 10/28 |
Section 2.3: More on compositions of linear transformations | Section 2.3: 1,4,12,17 |
| 10/30 |
Section 2.4: Invertibility and isomorphisms | Section 2.4: 1, 2(a)(c)(e),3,7,14,15,16,17 |
| 11/2 |
Section 2.5: Change of coordinates | Section 2.5: 1,2(a)(c),3(a)(c),5,7,10,13 |
| 11/3 (Tues) |
No quiz this week |
|
| 11/4 |
Midterm Exam | Midterm
Info Sample Problems |
| 11/6 |
Quotient spaces | 1. Complete the proof that the
quotient space V/W is a vector space. Namely, verify
the axioms (VS1)-(VS8) that were not verified in class. 2. Complete the proof that if f: V->W is a linear map, then V/Ker f is isomorphic to Im f. |
| 11/9 |
Section 4.4: Review of determinants | Section 4.4: 1,2,3(a)(c)(g),4(a),5,6 |
| 11/10 (Tues) |
Quiz 5 |
|
| 11/11 |
University Holiday
(Veterans Day) |
|
| 11/13 |
Section 5.1: Eigenvalues and
eigenvectors |
Section 5.1:
3(a)(b)(c)(d),4(a)(b)(e) |
| 11/16 |
Factoring
polynomials |
Section
5.1: 7,8,14,15(a),16(a),17,22,23 |
| 11/17 (Tues) |
Quiz 6 |
|
| 11/18 |
Section 5.2: Diagonalizability | Section 5.2:
1(a)-(g),3(a)(d)(e),8 |
| 11/20 |
Section 5.2: Some applications |
Section 5.2: 9(a),10,11,12,19 |
| 11/23 |
Section 5.2: Direct sum
decompositions |
Section 5.2:
1(h)(i),14,15,20,22 |
| 11/24 (Tues) |
Quiz 7 |
|
| 11/25 |
Section 6.1: Inner products |
Section 6.1: 1,2,3,4,6,8,9 |
| 11/27 |
No Class (Thanksgiving) |
|
| 11/30 |
Section 6.1: Inner products Section 6.2: Gram-Schmidt orthogonalization |
Section 6.1: 12,16,17,23 Section 6.2: 1(a)(b)(f)(g),2(b)(c)(g)(i) |
| 12/1 (Tues) |
Quiz 8 |
|
| 12/2 |
Section 6.2: Gram-Schmidt
orthogonalization |
Section 6.2:
4,5,6,7,9,13,19(c),21 |
| 12/4 |
Section 6.3: Adjoints |
Section 6.3:
1,2(a)(c),3(a)(c),4,14 |
| 12/7 |
Section 6.4: Self-adjoint and
normal operators |
Section 6.4: 1,2(a)(c)(d),4,5,9,12,16,20 (Note that we'll discuss normal operators next time) |
| 12/8 (Tues) |
Quiz 9 |
|
| 12/9 |
Section 6.4: Self-adjoint and
normal operators |
Start doing sample problems
for final exam |
| 12/11 |
Review/summary (we'll do some
sample problems) |
|
| 12/15 (Tues) | Final
Exam |
Final
Info Sample Problems |