Fall 2009 Linear Algebra

Last updated on Aug. 30, 2010.

Course Schedule
Time: Monday and Wednesday, 9:10 am–10:25 am
Location: Room 203, Mathematics Building
Instructor
Name: Weizhe Zheng
Office: Room 606, Mathematics Building; Phone: 212-854-3003
Email: zheng at math dot columbia dot edu
Office hours: Monday 3 pm–4 pm and Friday 9:30 am–10:30 am, in instructor's office
Teaching Assistants
Alexandru Georgescu Email: abg2129 at columbia dot edu; Help Room Hours: Tuesday 4 pm–5 pm and Thursday 5 pm–6 pm
Ion Mihalescu Email: igm2103 at columbia dot edu; Help Room Hours: Tuesday and Thursday, 4 pm–5 pm
Help Room
The Department of Mathematics maintains the Columbia Help Room for students needing help with their upper-level mathematics courses.
Hours: 10 am–6 pm Monday through Thursday, 11 am–4 pm Friday (detailed schedule of who will be staffing the room)
Location: Room 406, Mathematics Building
Textbook
Elementary Linear Algebra: A Matrix Approach, by Lawrence E. Spence, Arnold J. Insel, and Stephen H. Friedberg, 2nd edition, Prentice Hall, 2008. (Errata)
The book is available at the Columbia University Bookstore.
Grades
The overall course grade is determined as follows: Homework and exam grades will be posted on CourseWorks' Grade Book. Statistics will be posted here.
Syllabus
This syllabus is subject to change.
Date Topic Reading Homework
Sep. 9 vectors and matrices, linear combinations, matrix-vector products 1.1, 1.2, Proofs #1 due on Sep. 14
1.1: 6, 24, 33, *81, 82; 1.2: 6, 9, 33, 42
Sep. 14 systems of linear equations 1.3 #2 due on Sep. 21
1.2: 70, 80; 1.3: 6, 9, 32, 45, 77; 1.4: 10, 40, 47, 88
Sep. 16 Gaussian elimination 1.4
Sep. 21 Span and linear dependence 1.6, 1.7 #3 due on Sep. 28
1.6: 2, 17, 26, 67; 1.7: 5, 40, 55; 2.1: 1, 12, 27, 65
Sep. 23 matrix multiplication 2.1
Sep. 28 invertible and elementary matrices 2.3, 2.4 #4 due on Oct. 5
2.3: 3, 14, 27; 2.4: 10, 22, 67; 2.7: 1, 10, 60, 78; 2.8: 3, 24, 69
Sep. 30 linear transformations 2.7, 2.8
Oct. 5 determinants 3.1 #5 due on Oct. 12
3.1: 5, 20, 24, 37, 72, *80
Oct. 7 Midterm 1: covers Chapters 1 and 2 (except 1.5, 2.2, 2.5 and 2.6)
Oct. 12 determinants (cont'd) 3.2 #6 due on Oct. 19
3.2: 1, 18, 28, 63, 72, *82; 4.1: 5, 11, 26, 40, 77
Oct. 14 subspaces 4.1
Oct. 19 basis and dimension 4.2, 4.3 #7 due on Oct. 26
4.2: 5, 18, 63; 4.3: 10, 35, 63, 74; 4.4: 8, 30, 99; 4.5: 5, 15, 48
Oct. 21 coordinate systems 4.4, 4.5
Oct. 26 eigenvalues and eigenvectors 5.1 #8 due on Nov. 4
5.1: 1, 16, 29, 34, 69; 5.2: 15, 23, 38, 75, 78, *86
Oct. 28 characteristic polynomial 5.2
Nov. 4 diagonalization 5.3, 5.4 #9 due on Nov. 9
5.3: 17, 49, 64, 84, *88; 5.4: 26, 75
Nov. 9 the geometry of vectors 6.1 #10 due on Nov. 16
6.1: 5, 12, 41, 95
Nov. 11 Midterm 2: covers Chapters 3 to 5 (except 5.5)
Nov. 16 orthogonal vectors 6.2 #11 due on Nov. 23
6.2: 3, 14, 17, 55; 6.3: 3, 12, 19, *60, 68; 6.4: 3
Nov. 18 orthogonal projections 6.3, 6.4
Nov. 23 orthogonal matrices and operators 6.5 #12 due on Nov. 30
6.5: 6, 38, 44, 46, 54; 6.6: 18, 41, 48, *55, 59, 68
Nov. 25 symmetric matrices 6.6
Nov. 30 vector spaces and their subspaces 7.1 #13 due on Dec. 7
7.1: 2, 29, 60, 62, 91; 7.2: 1, 15, 25, 30, *49
Dec. 2 linear transformations 7.2
Dec. 7 basis and dimension 7.3, 7.4 #14 due on Dec 14
7.3: 3, 10, 51, 68; 7.4: 7, 14, 16, 42, 46; 7.5: 11, 47, 71, *81
Dec. 9 inner product spaces 7.5
Dec. 14 Review
* Starred problems are extra credit.
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