School of Engineering \ Computer Engineering
Course Credit
ECTS Credit
Course Type
Instructional Language
Programs that can take the course
Computer Engineering
Artificial Intelligence Engineering
This course presents the basics of linear algebra along with its applications. Topics include vectors, systems of linear equations, graphs and networks, linear transformations, vector spaces, the concept of orthogonality and Gram-Schmidt, determinants and spectral linear algebra. There is an emphasis on the applications of linear algebra on physical problems and computer science such as PageRank and singular value decomposition.
Textbook and / or References
• Gilbert Strang, Introduction to Linear Algebra, 5th Edition, Wellesley-Cambridge Press, (2016)
• Shayle Searle and André Khuri, Matrix Algebra Useful for Statistics, 2nd Edition, John Whiley and Sons, 2017
• David Lay, Steven Lay, and Judi McDonald, Linear Algebra and Its Applications, 5th Edition, Pearson, 2016
• Howard Anton, Chris Rorres, and Anton Kaul, 12th Edition, John Wiley and Sons, 2019
To learn the fundamentals of linear algebra from the definitions of vectors and matrices to operations on matrices, determinants, eigenvalues/eigenvalues of matrices including the applications of linear algebra to various filelds in computer/data/artificial engineering and others.
1. Learn how to solve linear systems.
2. Learn about vectors and matrices.
3. Understand four fundamental subspaces, rank, basis and independence.
4. Use linear algebra to model and solve physical problems.
5. Understand projections and how to solve least squares problems.
6. Learn eigenvalues, eigenvectors, diagonalization and how to solve systems of ordinary differential equations using matrix exponential.
7. Learn about singular value decomposition and PageRank.
Week 1: Vectors (Definitions, linear combinations, length, dot product, …)
Week 2: Matrices (Definitions, matrix arithmetic)
Week 3: Matrices (Definitions, matrix arithmetic)
Week 4: Systems of Linear Equations (geometry of linear equations, Gaussian elimination, matrix multiplication, …)
Week 5: Linear Transformations (rotations, general transformations)
Week 6: Vector Spaces (four subspaces, rank, reduced form, bases, …)
Week 7: Orthogonality (orthogonality of four subspaces, projections, least squares, …)
Week 8: Determinants (volume, cofactors and adjoint matrix, Cramer’s rule, …)
Week 9: Eigenvalues and eigenvectors (matrix diagonalization, symmetric and positive definite matrices, similar matrices, singular value decomposition)
Week 10: Applications: Graphs and networks; Markov chains; Linear algebra of functions; Computer Graphics; Deep Learning; …
Week 11: Applications: Graphs and networks; Markov chains; Linear algebra of functions; Computer Graphics; Deep Learning; …
Week 12: Applications: Graphs and networks; Markov chains; Linear algebra of functions; Computer Graphics; Deep Learning; …
Tentative Assesment Methods
Quizzes: 15 %
Lab: 15 %
Midterm: 30 %
Final: 40 %
|
Program Outcome
*
|
| 1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
|
Course Outcome
|
|---|
| 1 |
A
|
|
|
|
|
C
|
|
|
|
|
|
| 2 |
A
|
|
|
|
|
C
|
|
|
|
|
|
| 3 |
A
|
|
|
|
|
C
|
|
|
|
|
|
| 4 |
A, D, B
|
A, B
|
|
|
|
A, C
|
|
|
|
|
|
| 5 |
A
|
|
|
|
|
C
|
|
|
|
|
|
| 6 |
A, B
|
|
|
|
|
C
|
|
|
|
|
|
| 7 |
A, C, D
|
A, B
|
|
|
|
A, C
|
|
|
|
|
|