Lecture Schedule & Updates
- Wed. 1/26: Ch. 1.1. Definition of a vector space, examples.
HW problems Ch.1: #1.1-1.5 - Fri. 1/28: Ch. 1.2. Linear combinations, bases.
HW problems Ch.1: #2.1-2.3, 2.5. Try 2.6 if you can.Hint for 2.6: Can you write the v's in terms of the w's? What would that allow you to do?
- Mon. 1/31: Ch. 1.3. Linear transformations and matrices.
HW problems Ch.1: #3.1-3.5. Due Fri 2/4. - Wed. 2/2: Ch. 1.5. Composition of linear transformations and matrix products.
HW problems Ch.1: #5.1-5.5, 5.8. Due Fri 2/4. - Fri. 2/4: Ch. 1.6. Invertible transformations and matrices.
HW problems Ch.1: #6.1-6.4, 6.6, 6.10, 6.12. Due Fri 2/11.I will be out of town on Friday, consequently there will be no office hours, and Prof. Treil will fill in for me in the lecture. Homework can either be turned in during class, or to the Math 540-S02 box in the Math department mailroom (Kassar, 1st floor) by 4pm.
- Mon. 2/7: Ch. 1.7. Subspaces.
HW problems Ch.1: #7.1, 7.3-7.5, 6.9. Due Fri 2/11. - Wed. 2/9: Ch. 2.1,2.2. Systems of linear equations.
HW problems Ch.1: #6.5, 6.11. Ch.2: #2.1a,b,c,e, 2.2. Due Fri 2/11.New Office hours are M 10-11, W 11-12, F 1-2.
- Fri. 2/11: Ch. 2.3. Analysis of pivots.
HW problems Ch.2: #3.1, 3.3-3.6, 3.8, extra credit 3.9. Read Ch.2 sec. 4. Due Fri 2/18. - Mon. 2/14: Ch. 2.5. Dimension, finite-dimensional spaces. Finding inverse by row reduction (self-study section 4)
HW problems Ch.2: #4.1, 5.1, 5.3-5.6. Due Fri 2/18. - Wed. 2/16: Ch. 2.6. General solution of a linear system; introduction to rank.
HW problems Ch.2: #3.7, 5.2, 6.1-6.2. Due Fri 2/18. - Fri. 2/18: Ch. 2.7. Fundamental subspaces, rank theorem.
HW problems Ch.2: #7.1-7.3, 7.7, 7.13-7.15. Due Fri 2/25. - Mon. 2/21: No class (Brown holiday).
- Wed. 2/23: Ch. 2.8. Change of coordinate/basis formula.
HW problems Ch.2: #8.1-8.4, 8.6, 7.4, 7.5. Due Fri 2/25. - Fri. 2/25: Review for Midterm I (on Mon 2/28).
- Mon. 2/28:Midterm I.
- Wed. 3/2:Ch. 3.1-3.3. Introducing determinants.
HW problems Ch.3: #3.1-3.3, Ch.2: #8.5, Ch.1: #5.6. Due Fri 3/4.Update: Since I did not get as far as computing determinants by column reduction, you will not have to do #3.3 on this week's homework.
- Fri. 3/4:Ch 3.3. Determinants, continued.
- Mon. 3/7:Ch 3.4-3.5.
Existence and uniqueness of the determinant function,Cofactor expansion, Cramer's rule.
HW problems Ch.3: #3.4-3.9, 5.1-5.6, 7.4,7.5, Due Fri 3/11. - Wed. 3/9:Ch 3.4. Formal definition of the determinant function; permutations.
HW problems Ch.3: #4.1-4.4, Due Fri 3/11. - Fri. 3/11:Ch 4.1. Introduction to eigenvectors and eigenvalues.
HW problems Ch.4: #1.1-1.4, 1.6-1.8, 1.10. Due Fri 3/18. - Mon. 3/14:Ch 4.2. Diagonalization
HW problems Ch.4: #1.9, 2.1-2.5, 2.9, 2.10. Ex. credit: 1.11. Due Fri 3/18. - Wed. 3/16:Ch 4.2. Diagonalization continued
HW problems Ch.4: #2.6-2.8, 2.12-2.14 Due Fri 3/18. - Fri. 3/18:Ch 5.1. Introduction to inner product spaces.
HW problems Ch.5: #1.1-1.5, 1.7, 1.8 Due Fri 3/25. - Mon. 3/21:Ch 5.2. Cauchy-Schwarz, triangle inequality, parallelogram law, norms, orthogonal/orthonormal bases.
HW problems Ch.5: #1.6, 1.9, 2.1-2.3, 2.5, 2.6 Due Fri 3/25. - Wed. 3/23:Ch 5.3. Orthogonal projection, Gram-Schmidt orthogonalization.
HW problems Ch.5: #2.7, 2.8, 3.1-3.3, 3.5-3.7 Due Fri 3/25. - Fri. 3/25:Ch 5.4. Least squares approximation.
HW problems Ch.5: #2.9, 4.1-4.4 Due Fri 4/8. - Mon. 4/4:Ch 5.5. Adjoint of a linear transformation.
HW problems Ch.5: #5.1-5.6 Due Fri 4/8. - Wed. 4/6:Ch 5.6. Isometries and unitary operators.
HW problems Ch.5: #6.1, 6.3-6.7, 7.1 Due Fri 4/8. - Fri. 4/8:Ch 6.1, 6.2. Upper triangular (Shur) representation. Spectral theorem for self-adjoint transformations.
HW problems Ch.6: 1.1, 2.1, 2.3, 2.4, 2.6, 2.7, 2.8, 2.10 Due Wed 4/13. - Mon. 4/11:Ch 6.2, 6.3. Spectral theorem for normal operators. Introducing singular values (not on Friday's exam)
HW problems Ch.6: 2.2, 2.5, 2.9, 2.13, 2.14, 3.1, 3.8 Due Wed 4/13.Important: I will not be on campus on Friday, so there will be no office hours. Instead I will hold office hours on Thursday from 12-2. My collegue Robin Koycheff will proctor the exam.
Some practice problems for Friday's exam. These aren't meant to be exhaustive, but rather indicative of the types and difficulty of problems which will appear. If you feel comfortable with these, then you should be comfortable with the exam. Solutions will be posted later.
- Wed. 4/13: Exam 2 review. Material covered on the exam will be from Chapters 3.1-3.5, 4, 5.1-5.6, 6.1, 6.2 in the book.
Extra office hours Thursday 12-2. No office hours Friday.
- Fri. 4/15: Exam 2 in class.
- Mon. 4/18:Ch 6.3, 6.4 Singular value decomposition, Polar decomposition.
HW problems Ch.6: #3.3-3.9, 3.11, 3.13, 4.1, 4.3Due Fri 4/22.I did not get to section 6.4 in class, but you should read it. We may have to proceed rather quickly through it on Wednesday.
- Wed. 4/20:Ch 6.4, 6.5 Applications of SVDs, Structure of Orthogonal matrices
HW problems Ch. 6: #3.12, 4.1, 4.3 Due Fri 4/22. - Fri. 4/22:Ch 6.5, 6.6 Structure of Orthogonal matrices, Orientation
HW problems Ch.6: #6.1-6.5; Read Ch.7.1; Ch.7: #1.1-1.4 Due Fri 4/29. - Mon. 4/25:Ch 7.1,7.2 Bilinear and Quadratic forms, diagonalization.
HW problems Ch.7: #2.1, 2.2, extra credit problem on unitary similarity. Due Fri 4/29.We will continue to have class over reading period.
The last lecture will be 5/6, and 5/9 will be review. - Wed. 4/27:Ch 7.3 Sylvester's Law of Inertia
HW problems Ch.7: #4.1, 4.2. Due Fri 4/29. - Fri. 4/29:Ch 7.4 Sylvester's criterion for positivity, minimax characterization of eigenvalues.
Office hours change for Monday 5/9: Office hours will be 11am instead of 10am.
- Mon. 5/2:Ch 8.1, 8.2. Introduction to dual spaces.
Office hours at 11am instead of 10am
This will be the last new lecture of the class.
Wednesday 5/4 and Friday 5/6 will be review, and Monday 5/9 there will be no class.
- Wed. 5/4, Fri. 5/6: Review.
- Mon. 5/9, Wed. 5/11: Office hours 2-4pm. No class.
- Final Exam Fri. 5/13 2pm, BH 168
Good luck!