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:
**Tuesdays & Thursdays, 16:30 - 17:50**, in LTC - L2:
**Tuesdays & Thursdays, 09:00 - 10:20**, in LTD

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

Week 1:

- Lecture 1: Systems of linear equations
- Lecture 2: Row reduction to echelon form [demo]
- Practice Problems

- Lecture 3: Vectors in Euclidean space
- Lecture 4: Matrix-vector products, linear independence [demo]
- Practice Problems

- Lecture 5: More linear independence, linear transformations
- Lecture 6: One-to-one and onto functions
- Practice Problems

- Lecture 7: Matrix operations, matrix multiplication [demo]
- Lecture 8: Invertible functions and matrices
- Practice Problems

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

- Lecture 11: Introduction to determinants
- Lecture 12: Properties of determinants [demo]
- No graded Practice Problems in Week 6 (prepare for midterm instead)

- Lecture 13: Abstract vector spaces

- Lecture 14: More vector spaces, eigenvectors, eigenvalues [demo]
- Lecture 15: Diagonalizable matrices
- Practice Problems

- Lecture 16: Fibonacci numbers and diagonalization
- Lecture 17: Complex numbers [demo]
- Practice Problems

- Lecture 18: Properties of complex eigenvalues
- Lecture 19: Orthogonal vectors, orthogonal projections
- Practice Problems

- Lecture 20: Orthogonal projections, Gram-Schmidt process
- Lecture 21: Least-squares solutions [demo]
- Practice Problems

- Lecture 22: Symmetric matrices [demo]
- Lecture 23: Singular value decompositions
- Practice Problems

- Lecture 24: More on SVDs [demo]
- Lecture 25: Final review
- Some extra demonstrations: [multiplication] [geometry] [eigenvalues] [graphs] [interpolation]

The following is our primary textbook:

*Linear Algebra and its Applications*, 6th 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:

- 5%: online homework assignments
- 5%: offline homework assignments
- 30%: midterm examination
- 60%: final examination

There are two components to the homework in this course: **online** and **offline**.

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

- Online homework will be submitted using WebWork.
- These assignments will be due on
**Mondays at midnight**, starting**11 September**.

There is also a weekly offline component to the homework. Here are the relevant logistics:

- A list of practice problems will be posted each week with the lecture notes.
- Each week, choose
**four**practice problems and write down solutions. - You can earn extra credit by solving more practice problems. See the instructions.
- These assignments will be due on
**Wednesdays at midnight**, starting**13 September**.

- Date:
**October 17** - Time:
**(your lecture period)** - Location:
**(your lecture classroom)**

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]
- Practice Midterm 4 (midterm from fall 2021) [solutions]
- Practice Midterm 5 (midterm from fall 2022) [solutions]

Our 80 minute midterm will be a little shorter than these tests.

Here are solutions to the L1 midterm.

Here are solutions to the L2 midterm.

- Date:
**18 December** - Time:
**8:30AM - 11:30AM** - 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).

- 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 2021) [solutions]
- Practice Exam 4 (final exam from fall 2022) [solutions]

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)