Welcome to the homepage for Math 2121: Linear Algebra!

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

- L1: Mondays 1:30-2:50PM, Fridays 9:00-10:20AM, Lecture Theater C
- L2: Mondays 3:00-4:20PM, Fridays 10:30-11:50AM, Lecture Theater C
- L3: Mondays, Wednesdays 12:00-1:20PM, Room 4619, Lift 31-32

- Eric: Room 3492, Lift 25-26.
- Jian-Shu: Room 3458, Lift 25-26.

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

*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. The course can be accessed for free online and has many helpful videos, notes, and exercises.

Some students have recommended this YouTube channel dedicated to linear algebra topics.

Grades will be computed as follows:

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

- The midterm will be on
**19 October**from**10:00AM to Noon**, replacing Friday's lectures - Email your instructor right away if you have a conflict.
- Midterm location:
**Even student IDs: Lecture Theater B****Odd student IDs: Lecture Theater C**

- Information on what to study:
- The midterm will cover Lectures 1-11 and HW 1-6.
- Review problems [solutions]
- Practice Exam (midterm from last fall) [solutions]

- Midterm solutions

- Logistics for the final examination:
- Date:
**14 December** - Time:
**8:30 AM to 11:30 AM** - Location:
**S H Ho Sports Hall**

- Date:
- There will be no alternate exam times.
- Information on what to study:
- The final will cover Lectures 1-22 and all homework assignments.
- Review problems [solutions]
- Practice Exam (final from last fall) [solutions]

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, null and column space (reading: Sections 2.4, 2.8)
- Week 6: Dimension, rank, determinants (reading: Sections 2.9, 3.1-3.2)
- Week 7: Determinants, midterm (reading: Sections 3.1-3.2)
- Week 8: Vector spaces, eigenvectors, and eigenvalues (reading: Sections 4.1-4.6, 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)

- Week 1:
- Week 2:
- Week 3:
- (No lecture on Monday due to cancellation)
- Lecture 5: Linear independence, linear transformations, one-to-one and onto functions

- Week 4:
- Week 5:
- (No lecture on Monday due to public holiday)
- Lecture 8: Subspaces, null and column space of a matrix

- Week 6:
- Lecture 9: Dimension and rank
- Lecture 10: Introduction to the determinant

- Week 7:
- Lecture 11: Properties of the determinant
- (Midterm exam on Friday, no lectures on Wednesday/Friday)

- Week 8:
- Lecture 12: Vector spaces
- Lecture 13: Eigenvectors and eigenvalues

- Week 9:
- Lecture 14: Similar and diagonalizable matrices
- Lecture 15: Fibonacci numbers and repeated eigenvalues

- Week 10:
- Lecture 16: Complex eigenvalues
- Lecture 17: Eigenvalues, inner products

- Week 11:
- Lecture 18: Orthogonal vectors and orthogonal projections
- Lecture 19: More on projections, Gram-Schmidt process

- Week 12:
- Lecture 20: Least-squares solutions
- Lecture 21: Symmetric matrices

- Week 13:
- Lecture 22: Singular value decompositions
- Lecture 23: Final review

Homework will be submitted online using WeBWorK.

Assignments will be due at midnight each Tuesday.

- The first homework assignment will be due on
**11 September**. - No homework due on
**23 October**. - The last homework assignment will be due on
**29 November**.