Text: Linear Algebra (4th ed.), by Friedberg, Insel and Spence,
Prentice Hall, 2003 ISBN 0-13-008451-4.
Week | Lecture dates | Sections | topics |
---|---|---|---|
1 | 9/2 (W) | Chapter 1 | Abstract vector spaces & subspaces |
2 | 9/8 (T), 9 (W) | Chapter 1 | Span of subsets, linear independence |
3 | 9/14, 16 | Chapter 1 | Bases and dimension |
4 | 9/21, 23 | Chapter 2 | Linear transformations |
5 | 9/28, 9/30 | Chapter 2 | Change of basis, dual spaces |
6 | 10/5, 10/7 | Ch. 1—2 | Review and Exam 1 |
7 | 10/12, 10/14 | Chapter 3 | Rank and Systems of Linear Equations |
8 | 10/19, 10/21 | Chapter 4 | Determinants and their properties |
9 | 10/26, 10/28 | Chapter 5 | Eigenvalues/eigenvectors |
10 | 11/2, 11/4 | Chapter 5 | Cayley-Hamilton |
11 | 11/9, 11/11 | Chapter 7 | Jordan Canonical Form |
12 | 11/16, 11/18 | Chapter 7 | Rational Canonical Form |
13 | 11/23 | Ch. 3—5, 7 | Review and Exam 2 |
14 | 11/30, 12/2 | Chapter 6 | Inner Product spaces |
15 | 12/7, 12/9 | Chapter 6 | Unitary and Orthogonal operators |
17 | December 21 (Monday) | 4-7 PM | Final Exam |
HW Due | HW Problems (due Wednesdays |
---|---|
Sept. 16 | 1.2 #17; 1.3 #19,23; 1.4 #11,13; 1.5 #9,15 |
Sept. 23 | 1.6 # 20,21,26,29; 1.7 #5,6; Show that the power series {∑ r^nx^n : r≠0} are linearly independent in F[[x]]. |
Sept. 30 | 2.1 #3,11,28; 2.2 #4; 2.3 #12; 2.4 #15,17 |
October 7 | 2.5 #3(d),7(a,b),13; 2.6 #5,10; Show that F[x]* ≅ F[[x]]. |
October 21 | 3.1 #6,12; 3.2 #5(b,d,h),17; 3.3 #8,10; 3.4 #8,15
If an nxn matrix A has each row sum 0, some Ax=b has no solution. |
October 28 | 4.1 #10(a,c); 4.2 #23; 4.3 #12,22(c),25(c); 4.4 #6; 4.5 #11,12 |
Nov. 4 | 5.1 #3(b),20,21; 5.2 #4,9(a),12;
Show that the cross product induces an isomorphism between R³ and Λ²(R³). |
Nov. 11 | 5.2 #18(a),21; 5.3 #2(d,f); 5.4 #6(a),13,19,25 |
Nov. 18 | 7.1 #3(b),9(a),13; 7.2 #3,14,19(a); 7.3 #13,14;
Find all 4x4 Jordan canonical forms of T satisfying T²=T³. |
Dec. 7 | 6.1; #6,11,12,17; 6.2 #2a,6,11; 6.8 #4(a,c,d),11 |
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