# Math 2121 (Fall 2020)

### Overview

Welcome to the homepage for Math 2121: Linear Algebra!

• Send questions for the instructor to emarberg@ust.hk.
Check out the syllabus here.

### Course materials

Our lectures this semester will be online at the following times:

New lecture notes will be posted each Friday. Try to read these before class.

Week 1:

Week 2:
• Lecture 3: Vectors in Euclidean space
• Lecture 4: Matrix-vector products, linear independence
Week 3:
• Lecture 5: Linear independence, linear transformations
• Lecture 6: One-to-one and onto functions
Week 4:
• Lecture 7: Matrix operations, matrix multiplication
Week 5:
• Lecture 8: Invertible functions and matrices
• Lecture 9: Subspaces, null and column space
Week 6:
Week 7:
Week 8:
Week 9:
• Lecture 16: Fibonacci numbers and diagonalization
• Lecture 17: Complex numbers, complex eigenvalues
Week 10:
Week 11:
Week 12:
Week 13:

New feature this semester: I will be showing some interactive Pluto notebooks in class demonstrating linear algebra concepts in the Julia programming language. The plan is to make around one notebook per lecture, to be posted on the day of lecture (or as soon as available).

You can view these notebooks as static HTML pages, but you are strongly encouraged to install Julia and Pluto in order to run and modify the code in each notebook yourself. This may be useful for exploring ideas, checking homework problems, etc.

Week 1:
Week 2:
Week 3:
Week 4:
Week 5:
Week 6:
Week 7:
Week 8:
Week 9:
Week 10:
Week 11:
Week 12:
Week 13:

### Other resources

The following is our primary textbook:

• Linear Algebra and its Applications, 5th edition, by D. Lay, S. Lay, and J. McDonald

Some other online resources:

Grades will be computed as follows:

• 10%: homework assignments, weighted equally
• 30%: midterm examination
• 60%: final examination

### Homework

We will have weekly homework assignments. Here are the relevant logistics:

• Homework will be submitted online using WeBWorK.
• Assignments 1-6 will be due at midnight each Wednesday.
• Assignments 7-11 will be due at midnight each Friday.
• The first homework assignment will be due on 16 September.

### Midterm

We will have a 2-hour, out-of-class midterm:
• Date: Friday, 23 October 2020
• Time: 7:00PM-9:00PM
• Location: online (instructions TBA)
Email the instructor right away if you have a conflict with the midterm date.
The midterm will cover Lectures 1-12 and HW 1-6.

Review problems and practice exams:

### Final

We will have a 3-hour, out-of-class final examination:
• Date: Thursday, 17 December 2020
• Time: 4:30PM-7:30PM
• Location: online (instructions TBA)
The final exam with be conducted in Canvas.
The format will be similar to the midterm.
The exam will be cumulative, covering all lectures and homework.

Review problems:
Practice exams:

### Schedule

The following is a tentative course outline, with reading assignments from the textbook.

• Week 1: Linear systems, row reduction to echelon form (reading: Sections 1.1-1.2)
• Week 2: Vectors, matrix equations, linear independence (reading: Sections 1.3-1.5, 1.7)
• Week 3: Linear independence, linear transformations (reading: Sections 1.7-1.9)
• Week 4: Matrix multiplication, the inverse of a matrix (reading: Sections 2.1-2.3)
• Week 5: Subspaces, bases, dimension (reading: Sections 2.4, 2.8-2.9)
• Week 6: Determinants (reading: Sections 3.1-3.2)
• Week 7: Vector spaces, midterm (reading: Sections 4.1-4.6)
• Week 8: Eigenvectors, and eigenvalues (reading: Section 5.1)
• Week 9: Similarity and diagonalisable matrices (reading: Sections 5.2-5.4)
• Week 10: Complex eigenvalues, properties of eigenvalues (reading: Sections 5.5, 6.1)
• Week 11: Inner products, orthogonality, and projections (reading: Sections 6.1-6.3)
• Week 12: Gram-Schmidt process, least-squares problems (reading: Sections 6.4-6.6)
• Week 13: Symmetric matrices, SVDs (reading: Sections 7.1, 7.4)