Linear Algebra II |
| Math 306, Winter 2013, Prof. Sherman. [Email: sherman1] |
| Text: "Linear algebra done right", 2nd ed., by Sheldon Axler |
| Topics: We will cover Chapters 1-6, essentially an introduction to abstract vector spaces and their linear operators. |
| Classroom: 38-201 |
| Office Hours: M 4-5; T 10-11; R 4-5; F 10-11 |
| Exams: We will have two midterms, a final exam, and periodic homeworks. See below for exam and homework schedule. |
| Grade: Homework 22%, Midterm I 22%, Midterm II 22%, Final Exam 34% |
| Syllabus: Here is the syllabus I handed out on day 1. |
Schedule of lectures: |
| |
Monday |
Tuesday |
Thursday |
Friday |
| Jan 7-11 |
Definition of a vector space |
Examples and properties of vector spaces |
Subspaces |
Direct sums |
| Jan 14-18 |
Direct sums |
Span and linear independence |
Span and linear independence;
Bases |
HW 1 due
Bases and dimension |
| Jan 21-25 |
No Class |
Dimension |
Dimension |
HW 2 due
Dimension; Linear maps |
| Jan 28-Feb 1 |
Kernel and image; matrices |
Matrices; invertibility |
Review |
Midterm I |
| Feb 4-8 |
Polynomials |
Polynomials |
Invariant subspaces |
HW 3 due |
| Feb 11-15 |
Invariant subspaces; polynomials applied to operators |
Examples: eigenvalues and invariant subspaces |
|
HW 4 due
Upper triangular matrices |
| Feb 18-22 |
No Class |
Diagonal matrices |
Diagonal matrices; real invariant subspaces |
HW 5 due |
| Feb 25-Mar 1 |
|
Midterm II |
Inner products and norms |
Inner products and norms |
| Mar 4-8 |
Orthonormal bases |
Gram-Schmidt |
Gram-Schmidt; orthogonal projections |
HW 6 due
Orthogonal projections; minimization problems |
| Mar 11-15 |
Linear functionals and ajoints |
Linear functionals and ajoints |
|
|
|
Homework:
HW1: Chapter 1 # 1, 3-6, 8-9, 13-15 Due Friday Jan 18
HW2: Chapter 2 # 1, 2, 7-12, 14, 16 Due Friday Jan 25
HW3: coming soon...
HW4: ...
HW5: ...
HW6: ...
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| Practice problems: All problems from the book! |