Welcome to the homepage for Math 2121: Linear Algebra!

- Send questions for the instructor to
**emarberg@ust.hk**. - Send questions about grades to your TA.

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

- L1:
**Wednesdays & Fridays, 13:30 - 14:50**, online through Zoom Meeting in Canvas - L2:
**Mondays & Wednesdays, 12:00 - 13:20**, in LTG

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

Week 1:

- (No lecture on Wednesday due to holiday)
- Lecture 7: Matrix operations, matrix multiplication

- Lecture 8: Invertible functions and matrices
- (No lecture on Friday/Monday due to holiday)

- Lecture 9: Subspaces, null and column space
- Lecture 10: Dimension and rank

- Lecture 11: Introduction to determinants
- Lecture 12: Properties of determinants

- Lecture 13: Abstract vector spaces
- Lecture 14: Vector spaces, eigenvectors, eigenvalues

- Lecture 15: Eigenspaces and similarity
- Lecture 16: Fibonacci numbers and diagonalization

- Lecture 17: Complex numbers, complex eigenvalues
- Lecture 18: Properties of eigenvalues

- Lecture 19: Orthogonal vectors, orthogonal projections
- Lecture 20: Orthogonal projections, Gram-Schmidt process

- Lecture 21: Least-squares solutions
- Lecture 22: Symmetric matrices

- Lecture 23: Singular value decompositions
- Lecture 24: More on SVDs

I will be showing some interactive Pluto notebooks in class using the Julia programming language.

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 problems, and future reference. However, using these programming tools is completely optional and not necessary for the course.- Notebook 1: Introduction, linear systems, row operations [Pluto link]
- Notebook 2: Echelon form, row reduction, solving linear systems [Pluto link]
- Notebook 3: Vectors and linear combinations [Pluto link]
- Notebook 4: Preview of matrix multiplication [Pluto link]
- Notebook 5: Linear transformations, onto and one-to-one functions [Pluto link]
- Notebook 6: Matrix multiplication and random walks [Pluto link]
- Notebook 7: Geometry of invertible matrices [Pluto link]
- Notebook 8: Determinants as signed volumes [Pluto link]
- Notebook 9: Signs of determinants [Pluto link]
- Notebook 10: Eigenvectors for the Fourier transform [Pluto link]
- Notebook 11: Computing eigenvalues numerically [Pluto link]
- Notebook 12: Fundamental theorem of algebra [Pluto link]
- Notebook 13: Some spectral graph theory [Pluto link]
- Notebook 14: Random orthogonal matrices [Pluto link]
- Notebook 15: Random symmetric matrices [Pluto link]
- Notebook 16: Polynomial interpolation [Pluto link]
- Notebook 17: Applications of SVDs [Pluto link]

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:

- This is a great YouTube channel dedicated to linear algebra topics.
*Linear Algebra Done Right*by Axler is a useful supplementary textbook.- Khan academy has many good instructional videos on linear algebra.
- Check out HKUST professor Jeffrey Chasnov's Matrix Algebra for Engineers on Coursera.

Grades will be computed as follows:

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

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

- Homework will be submitted online using WeBWorK.
- Assignments will be due at
**midnight each Friday**. - If you need extra time, be sure to request this before the deadline.
- The first homework assignment will be due on
**9 September**.

- Date:
**Tuesday, 26 October 2021** - Time:
**7:00PM-9:00PM** - Location:
- LTJ (for section L1)
- Room 2303 (for tutorial T2A)
- Room 2404 (for tutorial T2B)
- Room 2405 (for tutorial T2C)

**check your tutorial**to report to the correct room.

The midterm will cover

Review problems and practice exams:

- Some review problems with solutions.
- Practice Midterm 1 (midterm from fall 2017) [solutions]
- Practice Midterm 2 (midterm from fall 2018) [solutions]
- Practice Midterm 3 (midterm from fall 2019) [solutions]

- Date:
**Saturday, 18 December 2021** - Time:
**12:30PM-3:30PM** - Location: S H Ho Sports Hall

The exam will be cumulative, covering all lectures and homework.

Review problems:

- Some review problems with solutions.
- More review problems (no solutions will be posted).

There is an optional WeBWorK assignment that goes with these problems.

If you complete this, then we will use your score to replace your lowest homework grade.

- Practice Exam 1 (final exam from fall 2017) [solutions]
- Practice Exam 2 (final exam from fall 2018) [solutions]
- Practice Exam 3 (final exam from fall 2019) is online in WeBWorK.

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)