Lecture Schedule / Homework assignments
- Wed 5/8: Final Exam 2-5pm in Foxboro auditorium, Kassar House.
- Fri 4/26: Non-diagonalizable linear recurrances.
Office hours schedule for reading period is as follows:
- Mon May 6, 12-2pm
- Wed May 8 10am-12pm
- Wed 4/24: Cayley-Hamilton Theorem, Linear Recurrances.
- Mon 4/22: Proof of the Jordan Canonical Form theorem.
HW problems: In the notes, C.3, C.5, C.6. Due Wednesday 4/24.Here is the proof of the Jordan Canonical Form theorem that I will cover today.
- Fri 4/19: Characteristic polynomials, Jordan form. The source
material for the rest of the class will be these
supplementary notes.
HW problems: In the notes, C.1, C.2, C.4. Due Wednesday 4/24. - Wed 4/17: pp. 152-154. Polar decomposition, continued, singular values.
HW problems Axler p. 158 #23, 27, 28, 29, 31, 32, 34. Due Wednesday 4/24. - Mon 4/15: pp. 147-150, 152-154. Isometries and the polar decomposition.
HW problems Axler p. 158 #17, 18, 19, 21, 24. Due Wednesday 4/17. - Fri 4/12: pp. 134-137, 144-146. The Spectral Theorem for self-adjoint operators. Positive operators.
HW problems Axler p. 158 #6, 7, 9, 11, 13. Due Wednesday 4/17. - Wed 4/10: pp. 130-137. Normal operators and the Spectral Theorem.
HW problems Axler p. 158 #1, 2, 3, 4, 5. Due Wednesday 4/17.
Homework from 4/5-4/8 due today. - Mon 4/8: pp. 120-121, 128-132. Adjoints continued. Self-adjoint and normal operators.
HW problems Axler p. 122 #24, 25, 26, 28, 29. Due Wednesday 4/10. - Fri 4/5: pp. 113-121. Orthogonal projections, linear functionals and adjoints.
HW problems Axler p. 122 #9, 10, 14, 17, A.8. Due Wednesday 4/10. - Wed 4/3: Exam II in class.
Homework from 3/22 due today. - Mon 4/1: pp. 107-111. Inner product spaces, continued.
No additional homework -- just study for the exam! - Mon 3/25 -- Fri 3/29: Spring Break.
- Fri 3/22: pp. 102-108. Norms and orthonormality.
HW problems Axler p. 122 #2, 4, 6, 8. Due Wednesday 4/3.Don't forget that Exam II will take place on Wednesday 4/3, the first Wednesday after spring break.
- Wed 3/20: No class
- Mon 3/18: pp. 97-106. Inner product spaces.
HW problems LADW p. 94 #5.2, 5.3 (optional bonus question #5.5), Axler p. 122 #1, 2. Due Friday 3/22.There will be no class or office hours on Wednesday. Your homework assignment will be due on Friday, and I will hold extra office hours on Friday morning at 11:15.
- Fri 3/15: LADW, pp. 86-92. The matrix determinant continued.
HW problems LADW p. 85 #3.4, 3.5, Axler p. 244, #2, 21. - Wed 3/13: LADW, pp. 82-85. The matrix determinant continued.
- Mon 3/11: LADW, pp. 75-82. The matrix determinant.
HW problems LADW p. 85 #3.1, 3.2, 3.3.Rather than follow Axler's discussion of the determinant, which requires things we have not yet proved, we will follow professor Treil's book Linear Algebra Done Wrong, which can be downloaded for free at the linked page. We will cover Chapter 3, parts 1-3.
- Fri 3/8: pp. 87-93. Diagonal matrices continued, invariant subspaces for real matrices.
HW problems Ch. 5 #15, 16, 17, 18, 19, 20. Due Wed 3/13. - Wed 3/6: pp. 84-87. Eigenvectors and eigenvalues continued -- upper triangular matrices.
Homework from 3/1-3/4 due today.
HW problems Ch. 5 #10, 11, 12, 14. Due Wed 3/13. - Mon 3/4: pp. 79-84. Eigenvectors and eigenvalues continued.
HW problems Ch. 5 #5, 6, 7, 8, 9. Due Wed 3/6. - Fri 3/1: pp. 69-72, 76-79. Real roots of polynomials. Introduction to Eigenvectors: invariant subspaces.
HW problems Ch. 4 #4, Ch. 5 #2, 3, 4. Due Wed 3/6. - Wed 2/27: Exam I in class.
Homework from 2/20-2/22 due today.Solutions to Exam I.
- Mon 2/25: pp. 63-68. Polynomials.
- Fri 2/22: Row reduction and echelon form continued.
HW problems #1-5 in the row reduction notes.2/23: The row reduction notes have been updated to include both lectures and some homework problems.
- Wed 2/20: Row reduction and echelon form.
Homework from 2/13-2/15 due today.
HW problems p. 59 #20, 21, A.4. Due Wed 2/27.Office hours today at 3pm instead of 11am.
Here are some notes on row reduction.
- Mon 2/18: No class -- holiday.
- Fri 2/15: pp. 53-58. Invertibility.
HW problems p. 59 #22, 23, 24, 25. Due Wed 2/20. - Wed 2/13: pp. 53-58. Matrices continued. Invertibility.
Homework from 2/6-2/11 due today.
HW problems p. 59 #16, 17, 18. Due Wed 2/20. - Mon 2/11: pp. 46-53. Consequences of Rank Theorem, matrices.
HW problems p. 59, #4, 9, 10. Due Wed 2/13. - Fri 2/8: Brown cancelled due to blizzard.
pp. 46-53. Consequences of Rank Theorem, matrices. - Wed 2/6: pp. 42-45. Null spaces and the Rank Theorem.
Homework from 1/30-2/4 due today.
HW problems p. 35, #13, 14, 16, 17. p. 59, #1, 2, 3. Due Wed 2/13. - Mon 2/4: pp. 38-41. Linear maps.
HW problems p. 35, #10, A.2, A.3. Due Wed 2/6.We are one class ahead of the other section, so the homework problems are currently one class behind.
- Fri 2/1: pp. 32-34,
38-39. Bases and dimension wrapped up.Intro. to linear maps.
HW problems p. 35, #6, 8, 9. Due Wed 2/6. - Wed 1/30: pp. 25-32. Bases and dimension.
Homework from 1/23-1/28 due today.
HW problems p. 35, #2, 3, 4. Due Wed 2/6. - Mon 1/28: pp. 21-24. Finite dimensional vector spaces.
HW problems p. 35 #1, A.1. Due Wed 1/30. - Fri 1/25: pp. 11-18. Properties of vector spaces, subspaces, direct sums.
HW problems p. 19 #4, 5, 6, 7, 8, 9. Due Wed 1/30. - Wed 1/23: pp. 1-10. Definition of a vector space.
HW problems p. 19 #1, 2, 3. Due Wed 1/30.