### Basic Information

- Course: Linear Algebra II
- Lecture: MWF, 3:00 – 3:50 PM, A328 Wells Hall
- Textbook:
*Linear Algebra Done Right*, 3rd Edition, by Sheldon Axler - Syllabus
- Office hours are held in my office, C303 Wells Hall, at the following times:
- Tuesday, 3:00 PM – 4:00 PM
- Wednesday, 2:00 PM – 3:00 PM
- Thursday 4:00 PM – 5:00 PM

### Reading Schedule

- Immediately: 1.A (
**R**^n and**C**^n) - By Friday, September 11: Chapter 4 (Polynomials)
- Lecture 01 (September 2): 1.B (Definition of Vector Space)
- Lecture 02 (September 4): 1.C (Subspaces) & 2.A (Span and Linear Independence)
- Lecture 03 (September 9): 2.B (Bases)
- Lecture 04 (September 11): 2.C (Dimension)
- Lecture 05 (September 14): 3.A (The Vector Space of Linear Maps)
- Lecture 06 (September 16): 3.B (Null Spaces and Ranges)
- Lecture 07 (September 18): 3.C (Matrices)
- Lecture 08 (September 21): 3.D (Invertibility and Isomorphic Vector Spaces)
- Lecture 09 (September 23): 5.A (Invariant Subspaces)
- Lecture 10 (September 25): Start 5.B (Eigenvectors and Upper-Triangular Matrices)
- Lecture 11 (September 28): Finish 5.B (Eigenvectors and Upper-Triangular Matrices)
- Lecture 12 (September 30): Review 5.B (Eigenvectors and Upper-Triangular Matrices)
- Lecture 13 (October 2): Start 5.C (Eigenspaces and Diagonal Matrices)
- Lecture 14 (October 5): Finish 5.C (Eigenspaces and Diagonal Matrices)
- Lecture 15 (October 7): Start 6.A (Inner Products and Norms)
- Lecture 16 (October 9): Middle 6.A (Inner Products and Norms)
- Lecture 17 (October 12): Midterm 1 (Chapters 1-5)
- Lecture 18 (October 14): Review of Midterm 1
- Lecture 19 (October 16): Finish 6.A (Inner Products and Norms)
- Lecture 20 (October 19): Start 6.B (Orthonormal Bases)
- Lecture 21 (October 21): Middle 6.B (Orthonormal Bases)
- Lecture 22 (October 23): Finish 6.B (Orthonormal Bases)
- Lecture 23 (October 26): Start 6.C (Orthogonal Complements and Minimization Problems)
- Lecture 24 (October 28): Finish 6.C (Orthogonal Complements and Minimization Problems)
- Lecture 25 (October 30): Start 7.A (Self-Adjoint and Normal Operators)
- Lecture 26 (November 2): Middle 7.A (Self-Adjoint and Normal Operators)
- Lecture 27 (November 4): Finish 7.A (Self-Adjoint and Normal Operators)
- Lecture 28 (November 6): Start 7.B (The Spectral Theorem)
- Lecture 29 (November 9): Middle 7.B (The Spectral Theorem)
- Lecture 30 (November 11): Finish 7.B (The Spectral Theorem)
- Lecture 31 (November 13): Start 7.C (Positive Operators and Isometries)
- Lecture 32 (November 16): Finish 7.C (Positive Operators and Isometries)
- Lecture 33 (November 18): Rigid Motions (Not in the textbook)
- Lecture 34 (November 20): Start 7.D (Polar Decomposition)
- Lecture 35 (November 23): Midterm 2
- Lecture 36 (November 25): Discussion of Rigid Motion Practice Problems
- Lecture 37 (November 30): Finish 7.D (Singular Value Decomposition)
- Lecture 38 (December 2): Applications of the Singular Value Decomposition (Image of the Unit Ball)
- Lecture 39 (December 4): Applications of the Singular Value Decomposition (Operator Norm)
- Lecture 40 (December 7): Applications of the Singular Value Decomposition (Matrix Form of SVD/Condition Number)
- Lecture 41 (December 9): Applications of the SVD (Condition Number) / Bilinear Forms
- Lecture 42 (December 11): Bilinear Forms and Quadratic Forms

### Lecture Notes

- Lecture 01 (September 2)
- Lecture 02 (September 4)
- Lecture 03 (September 9)
- Lecture 04 (September 11)
- Lecture 05 (September 14)
- Lecture 06 (September 16)
- Lecture 07 (September 18)
- Lecture 08 (September 21)
- Lecture 09 (September 23)
- Lecture 10 (September 25)
- Lecture 11 (September 28)
- Lecture 12 (September 30)
- Lecture 13 (October 2)
- Lecture 14 (October 5)
- Lecture 15 (October 7)
- Lecture 16 (October 9)
- Lecture 17 [Midterm 1] (October 12)
- Lecture 18 [Midterm 1 Solutions] (October 14)
- Lecture 19 (October 16)
- Lecture 20 (October 19)
- Lecture 21 (October 21)
- Lecture 22 (October 23)
- Lecture 23 (October 26)
- Lecture 24 (October 28)
- Lecture 25 (October 30)
- Lecture 26 (November 2)
- Lecture 27 (November 4)
- Lecture 28 (November 6)
- Lecture 29 (November 9)
- Lecture 30 (November 11)
- Lecture 31 (November 13)
- Lecture 32 (November 16)
- Lecture 33 (November 18)
- Lecture 34 (November 20)
- Lecture 35 [Midterm 2] (November 23)
- Lecture 36 [Discussion of Rigid Motion Practice Problems] (November 25)
- Lecture 37 (November 30)
- Lecture 38 (December 2)
- Lecture 39 (December 4)
- Lecture 40 (December 7)
- Lecture 41 (December 9)
- Lecture 42 (December 11)
- Entire Course

### Homework

- Homework 01 (due September 18) [Problems graded: 1.C: 12, 23; 2.A: 11; 2.C: 14]
- Homework 02 (due September 25) [Problems graded: 3.B: 6, 12, 24; 3.C: 6]
- Homework 03 (due October 2) [Problems graded: 3.D: 6; 5.A: 7, 16]
- Homework 04 (due October 9) [Problems graded: 5.B: 11; 5.C: 5, 10, 13]
- Homework 05 (due October 23) [Problems graded: 6.A: 6, 9, 18, 22, 25, 28]
- Homework 06 (due October 30) [Problems graded: 6.B: 5, 7, 12, 13, 14, 16]
- Homework 07 (due November 6) [Problems graded: 6.C: 5, 7, 8, 9, 10, 12, 14]
- Homework 08 (due November 13) [Problems graded: 7.A: 2, 6, 15, 17, 19, 21]
- Homework 09 (due November 20)
- Homework 10 (due December 4)
- There is no Homework 11. Rather, complete the “take home” portion of Midterm 2 (see below).

### Exams

- Midterm 1
- Date, time, and place: Monday, October 12, 3:00 PM – 3:50 PM, A328 Wells Hall
- Material covered: Chapters 1-5
- Exam
- Exam+Solutions

- Midterm 2
- Date, time, and place: Monday, November 23, 3:00 PM – 3:50 PM, A328 Wells Hall
- Material covered: Chapter 6, Chapter 7 (7.A, 7.B, 7.C), Rigid Motions
- Exam
- Instructions for “take home” retry portion (due December 11)
- Solutions

- Final Exam
- Date, time, and place: Thursday, December 17, 3:00 PM – 5:00 PM, A328 Wells Hall
- Material covered: The entire course, including Chapters 1-7, Rigid Motions, SVD applications, bilinear and quadratic forms
- Exam+Solutions

### Checkpoints

- Checkpoint 1: October 16. Includes homework assignments 01-04 and Midterm 1. Theoretical curve would be (please check D2L for your raw score):
- 70-100: 4.0
- 62-70: 3.5
- 56-62: 3.0
- 50-56: 2.5
- 44-50: 2.0
- 35-44: 1.5
- 25-35: 1.0
- 0-25: 0.0

- Checkpoint 2: December 13. Includes all homework assignments (1-10), Midterm 1, and Midterm 2 (in class and take home portions). Theoretical curve would be (please check D2L for your raw score):
- 68-100: 4.0
- 62-68: 3.5
- 56-62: 3.0
- 50-56: 2.5
- 44-50: 2.0
- 38-44: 1.5
- 32-38: 1.0
- 0-32: 0.0

- Course curve: December 22. Includes all graded material from the course, including the final exam.
- 66-100: 4.0
- 60-66: 3.5
- 54-60: 3.0
- 48-54: 2.5
- 42-48: 2.0
- 36-42: 1.5
- 30-36: 1.0
- 0-30: 0.0