# 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.