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.

The time and locations of the lectures are as follows:

- L1:
**Wednesdays & Fridays, 1:30-2:50PM, Lecture Theater C** - L2:
**Mondays & Wednesdays, 10:30-11:50AM, Lecture Theater C**

My office is Room 3492 in the Mathematics Department, near Lift 25-26.

Drop by anytime, or send an email to make an appointment.

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:

*Linear Algebra Done Right*by Axler is a great supplementary textbook.- Khan academy has many good instructional videos on linear algebra and other topics.
- HKUST professor Jeffrey Chasnov has launched a Coursera course called Matrix Algebra for Engineers which covers some of the same material as our class.
- This is a great YouTube channel dedicated to linear algebra topics.

Grades will be computed as follows:

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

We will have a 2-hour, out-of-class midterm:

- Date:
**Sunday, 20 October 2019** - Time:
**2:30-4:30PM** - Location:
- L1:
**Lecture Theater B** - L2:
**Lecture Theater J**

- L1:

Information on what to study:

- The midterm will cover Lectures 1-12 and HW 1-6.
- Review problems [solutions]
- Practice Exam 1 (midterm from fall 2017) [solutions]
- Practice Exam 2 (midterm from fall 2018) [solutions]

Our postponed 3-hour final examination is now scheduled:

- Date:
**Thursday, 20 February 2020** - Time:
**8:30-11:30AM**

Information on what to study for the final:

- The final exam will be cumulative, covering all lectures and homework assignments.
- Review problems [solutions]
- Practice Exam 1 (final exam from fall 2017) [solutions]
- Practice Exam 2 (final exam from fall 2018) [solutions]

Review assignments:

- We will post a few optional review assignments during the four weeks before the exam.
- If you complete the assignments then you can earn a small amount of extra credit for the final exam.
- Review Assignment 1.
- Review Assignment 2.
- Review Assignment 3.
- Review Assignment 4.

The following is a tentative course outline:

- 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)

Lectures notes will be posted online each Friday for the following week.

You should try to read the notes before each class.

- Week 1:
- Week 2:
- Week 3:
- Week 4:
- Week 5:
- Lecture 9: Subspaces, null and column space of a matrix
- Lecture 10: Dimension and rank

- Week 6:
- Lecture 11: Introduction to determinants
- Lecture 12: Properties of determinants

- Week 7:
- Lecture 13: Abstract vector spaces

- Week 8:
- Lecture 14: Vector spaces, eigenvectors, eigenvalues
- Lecture 15: Eigenspaces and similarity

- Week 9:
- Lecture 16: Diagonalization
- Lecture 17: Complex numbers

- Week 10:
- Lecture 18: Properties of eigenvalues
- Lecture 19: Orthogonal vectors and orthogonal projections [video]

- Week 11:
- Lecture 20: Orthogonal projections, Gram-Schmidt process [video (L1)] [video (L2)]

- Week 12:
- Lecture 21: Least-squares solutions [video]
- Lecture 22: Symmetric matrices [video]

- Week 13:
- Lecture 23: Singular value decompositions [video]
- Lecture 24: Final review

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 Tuesday.
- The first homework assignment will be due on
**10 September**. - There will be no homework assignment due on
**22 October**. - There will be no homework assignment due on
**19 November**. - The last homework assignment will be due on
**3 December**.