Topic outline

  • General

    MS-C1342 Linear Algebra

    • Period V: 24 April - 9 June 2023
    • Lecturer: Vanni Noferini, vanni dot noferini at aalto dot fi
    • Head assistant: Juha-Pekka Puska, juha hyphen pekka dot puska at aalto dot fi
    • Registration in Sisu
    • In 2023 lectures and exercise sessions will be held in person at the Aalto campus.
    • Instructions for the exercises are in the Assignments section.
    How to pass the course

    There are two options. A student can either return homework exercises and attend a final exam, or just attend the exam. In the first option, the homework and the exam are weighted at 40 and 60 percent respectively; in the second option, the final mark is 100 percent from the exam. As the final exam will be more difficult than the homework, the first option is highly recommended.

    The first option is only valid for the course exam (first exam right after the course). In later examinations, only the 100 percent exam option is available.

    Exceptions to this rule can be granted only if a student was forced to miss the course exam for impediments clearly beyond the student's control. A summer job is not considered an impediment beyond the student's control: generally, it is the student's responsibility to only start a summer job after all courses and exams are over, or alternatively to negotiate time off with the employer.


    Tentative Schedule

    • Week 1: Existence and uniqueness of solutions to the linear system Ax=b. Vector norms.

    • Week 2 : Inner product, operator norm, matrix norms.

    • Week 3: Stability of linear system Ax=b. Condition number. Eigenvalues, eigenvectors, eigendecompositions.

    • Week 4: Eigenvalue theory for Hermitian matrices, similarity, matrix exponential.

    • Week 5: Linearization of differential equations, least squares method, projection matrices.

    • Week 6: Gram-Schmidt orthogonalization, QR decomposition, Singular value decomposition.

    Additional reading material

    The lecture notes that can be found on the course's web pages provide sufficient knowledge to successfully pass the course. However, for those students who would like to have additional resources that complement and expand on the lecture notes, the following sources are recommended:

    For the theoretical parts: Gilbert Strang, "Introduction to Linear Algebra", Chapters 3, 4, 6, 7, 9
    For the computational parts: Lloyd N. Trefethen and David Bau, "Numerical Linear Algebra", Lectures 1, 2, 3, 4, 6, 7, 8, 12, 20 and 24

    Both books are available in the University's libraries. Please note that some of this suggested material goes way beyond what is covered in the lecture notes, and it is intended as additional reading material to gain further insight on the topics, and also for further/deeper personal study. I have provided these suggestions at the request of some students, and reading them could be helpful, but it is not compulsory.