ASE2010: Applied Linear Algebra

Course Info.

Course descriptions

• This course is about the central mathematical technique for all engineering disciplines: linear algebra. The course covers basics of vectors and matrices, linear independence, orthogonality, linear equations, least-squares methods, and many applications. We talk about the mathematics, but the focus will be on conceptual understanding and using those in applications such as dynamics, control, estimation, and machine learning. Students will also work on computational homework assignments where they use Python to do computations with vectors, matrices, and least squares methods for solving practical engineering problems.

Instructors

• Instructor: Jong-Han Kim (Rm.507 @aerospace campus)

• TA: Jun-Hyon Cho (Rm.502 @aerospace campus)

• TA: Jin Choi (Rm.502 @aerospace campus)

Lectures

• Tue/Thr 10:30-11:45 (Rm.216 @aerospace campus)

Office hours

• JHK: Tue/Thr 16:00-17:00 (Rm.507), or by appointments.

Prerequisites

• Previous exposure to calculus, engineering mathematics, and programming language (Python or others).

• You do not need to have any background knowledges on a variety of engineering application, however interest in them will definitely be a plus.

Reference textbooks

• Introduction to applied linear algebra - vectors, matrices, and least squares, by Boyd and Vandenberghe. Available online.

• Linear algebra and learning from data, by Strang.

Grading policy

• Final exam (40%)

• Midterm exam (30%)

• Homework assignments and class participation (30%)

Lecture notes

Some of the course material is reproduced from the Engr108: Introduction to matrix methods by Stephen Boyd at Stanford university, under his kind permission.

1. Vectors

2. Linear functions

3. Norm and distance

4. Clustering

5. Linear independence

6. Matrices

7. Matrix examples

8. Linear equations

9. Linear dynamical systems

10. Matrix multiplication

11. Matrix inverses

12. Least squares

13. Least squares data fitting

14. Least squares classification

15. Multi-objective least squares

16. Constrained least squares

17. Constrained least squares applications

Assignments

1. HW#1 (due 9/14)

2. HW#2 (due 9/30)

3. HW#3 (due 10/12)

4. HW#4 (due 10/19)

5. HW#5 (due 10/26)

6. HW#6 (due 11/21)

7. HW#7 (due 12/12)

Computational examples

The link directs to the associated Jupyter notebook file, which opens on Google Colaboratory when the “Open in Colab” button is clicked.

1. \(k\)-means clustering (and elements of unsupervised learning)

2. Document recommenation system (clustering over word count vectors)

3. Stage illumination

4. Model fitting

5. Handwritten image classifier

6. Ridge regression

7. Minimum energy control

Exam

1. Final exam (Autumn 2023)

Sample Exams

1. Midterm exam (2021) and solutions