Instructor: Ljudmila Kamenova
Office: Math Tower 3-115
Office hours: MW 10-11am in Math Tower 3-115; F 10-11am - administrative advising hours; or send me an e-mail: kamenova@math.stonybrook.edu.
TAs: Matthew Huynh and Connor Lehmacher
TAs office hours: Matthew Huynh's web card
and Connor Lehmacher's web card
Course Description:
Finite dimensional vector spaces, linear maps, dual spaces, bilinear functions, inner products. Additional topics include canonical forms, multilinear algebra, numerical linear algebra.
Major Topics Covered: Matrices and Operations on Matrices; Determinants of Matrices; Vector Spaces and Subspaces; Linear Transformations and Linear Operators; Kernels and Images; Basis for Vector Space and the Dimension of a Vector Space; Eigenvalues, Eigenvectors and the Diagonalization of Linear Operators; the Cayley-Hamilton Theorem; Inner Product Spaces; Selfadjoint Operators, Normal Operators, and Orthogonal Operators; the Spectral Theorem.
Textbook: Linear Algebra Done Right (3rd Ed.), by Sheldon Axler, Springer 2014.
Sheldon Axler's videos accompanying his book: https://linear.axler.net/LADRvideos.html
Grading: Homework accounts for 30% of the total grade; each Midterm is worth 20% of the total grade; the Final is worth 30% of the total grade.
| Week. | Lecture Dates. | Topics covered from the Textbook. |
|---|---|---|
| 1. | Aug 28 - Sept 1. | Intro to course, R^n and C^n, Vector spaces and subspaces (1.A, 1.B, 1.C) |
| 2. | Sept 4 - 8. | No class on Labor Day, Sept 4. More on subspaces (1.C, 2.A) |
| 3. | Sept 11 - 15. | Direct sums, Linear independence and span (2.A) |
| 4. | Sept 18 - 22. | Bases and dimension, Linear maps (2.B, 2.C, 3.A) |
| 5. | Sept 25 - 29. | More linear maps, Null space and range, Matrices (3.A, 3.B, 3.C) |
| 6. | Oct 2 - 6. | More matrices and invertibility, Products and quotients (3.C, 3.D, 3.E) |
| 7. | Oct 9 - 13. | Fall break - no class on Oct 9. Polynomials and complex numbers (4) |
| 8. | Oct 16 - 20. | MIDTERM 1 on Oct 16 in class (covers up to 3.E), Invariant subspaces and eigenvalues/vectors (5.A) |
| 9. | Oct 23 - 27. | Upper triangular matrices from eigenvectors, Understanding diagonalization (5.B, 5.C) |
| 10. | Oct 30 - Nov 3. | Inner products and norms, Triangle inequality, Orthonormal bases (6.A, 6.B) |
| 11. | Nov 6 - 10. | Applications of orthonormal bases, Orthogonal complements, Minimization, Adjoints (6.B, 6.C, 7.A) |
| 12. | Nov 13 - 17. | Self-adjoint and normal operators (7.A). MIDTERM 2 on Nov 15 in class (up to 6.C, no 3.F) |
| 13. | Nov 20 - 24. | The spectral theorem (7.B). Thanksgiving break - no classes Nov 22 - 24. |
| 14. | Nov 27 - Dec 1. | Proof of the real spectral theorem, Generalized eigenvectors (8.A, 8.B) | 15. | Dec 4 - 7. | Characteristic and minimal polynomials, Jordan form (8.C, 8.D) |
| 16. | Dec 11. | Review in class by Connor (last day of classes). |
| 17. | Dec 13. | Final exam: 11:15am-1:45pm, in the classroom. |
Homework is a fundamental part of this course. Late homework will not be accepted. Homework will account for 30% of the total grade. The exercises will be taken from the course textbook. Homework is due in your recitation in the week indicated below and should be handed to your recitation instructor.
| Number. | Due Week (in recitation). | Exercises from the textbook. |
|---|---|---|
| 1. | Week of Sept 11 in recitation.. | Problems 1.A.2, 1.B.2, 1.B.5, 1.C.12, 1.C.19. |
| 2. | Week of Sept 18 in recitation.. | Problems 1.C.20, 2.A.6, 2.A.10, 2.A.14, 2.A.15. |
| 3. | Week of Sept 25 in recitation.. | Problems 2.B.3, 2.B.6, 2.C.1, 2.C.10, 2.C.12. |
| 4. | Week of Oct 2 in recitation.. | Problems 3.A.1, 3.A.7, 3.A.11, 3.B.6, 3.B.13. |
| 5. | Week of Oct 23 in recitation.. | Problems 3.C.2, 3.D.9, 3.D.18, 3.E.2, 3.E.7. | 6. | Week of Oct 30 in recitation.. | Problems 4.4, 4.6, 5.A.8, 5.A.9, 5.A.15a (i.e., only part (a) of problem 5.A.15). | 7. | Week of Nov 6 in recitation.. | Problems 5.B.2, 5.B.4, 5.B.7, 5.C.1, 5.C.9. | 8. | Week of Nov 20 in recitation.. | Problems 6.A.8, 6.A.10, 6.B.2, 6.B.5, 6.C.2. | 9. | Week of Nov 27 in recitation.. | Problems 7.A.1, 7.A.2, 7.A.5, 7.B.2, 7.B.6. | 10. | Week of Dec 4 in recitation.. | Problems 8.A.2, 8.A.3, 8.A.8, 8.B.1, 8.B.2. |
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