MS-A0011: Matrix Algebra
| Course name | Matrix Algebra |
|---|---|
| Course code | MS-A0011 |
| Abbreviation | |
| Period | II |
| Lecturer | Chris Bruzska |
Description
Matrix Algebra is a 5 ECTS service course offered by the Department of Mathematics and Systems Analysis, taken by students across the School of Science and other Aalto schools. The course covers the core topics of linear algebra: vector computations, matrix operations, systems of linear equations, and eigenvalues. After completing the course, students can write systems of linear equations in matrix form, solve them via Gaussian elimination, perform basic matrix operations, compute eigenvalues of square matrices, and understand the significance of matrix decompositions.
Course material
Official material
The course does not have a single mandatory textbook. Lecture slides and notes are distributed through MyCourses. Weekly exercise sheets form the core of independent study. Some iterations of the course reference standard linear algebra texts for additional reading, but these are optional.
Extra material
The freely available lecture notes by Gilbert Strang (MIT OpenCourseWare, 18.06) are an excellent supplement and cover the same topics at a comparable level.
Contents and workload
Overall workload
The weekly intensity is noticeably higher, expect around 12–15 hours per week. The workload is fairly uniform: each week introduces new theory and a corresponding exercise sheet. The pace is fast, and concepts build on each other, so keeping up is essential. Students who revisit the theory before attempting exercises tend to do significantly better.
Weekly contents
| Week | Topics |
|---|---|
| 1 | Vectors in $\mathbb{R}^n$; vector addition and scalar multiplication; dot product; geometric interpretation. |
| 2 | Matrices; matrix addition and multiplication; transpose; identity and zero matrices. |
| 3 | Systems of linear equations; matrix form $Ax = b$; Gaussian elimination; row echelon form. |
| 4 | Matrix inverses; conditions for invertibility; the inverse via row reduction; LU decomposition basics. |
| 5 | Linear independence; span; basis and dimension of a vector space; rank of a matrix. |
| 6 | Eigenvalues and eigenvectors; characteristic polynomial; diagonalisation. |
| 7 | Applications and wrap-up; matrix decompositions (overview of SVD); revision for exam. |
Practicalities
The course is completed via weekly exercise sessions and a final course exam (or alternatively, exam only). Lectures are held twice a week and exercise sessions once or twice a week, depending on the period. The exam is written and closed-book; a formula sheet is typically not provided, so key formulas should be memorised. Partial credit is given on exercises. There is also a Laskutupa (drop-in maths help centre) available to students in all MS-A courses.
Related courses
Official prerequisites
Additional prerequisites
Comfort with algebraic manipulation and working with equations. Students who struggled with mathematics in high school may want to revise equation systems and basic algebra before the course begins.
More like this
- MS-A0111 Differential and Integral Calculus 1 — the companion first-year mathematics course, typically taken in the same year.
- MS-A0211 Differential Equations — natural follow-up where linear algebra tools are applied.
- MS-C1342 Linear Algebra — a more rigorous and abstract treatment for students who want to go deeper.
- CS-A1110 Programming 1 — commonly taken in parallel during the first year.