Topic outline

  • General

    MS-C1342 Linear Algebra

    • Period V: 22 April - 7 June 2024
    • Lecturer: Vanni Noferini, vanni dot noferini at aalto dot fi
    • Guest lecturer (Week 4 only): Paul Van Dooren, vandooren dot p at gmail dot com
    • Head assistant: Ryan Wood, ryan dot wood at aalto dot fi
    • Registration in Sisu
    • In 2024 lectures and exercise sessions will be held in person at the Aalto campus.
    • Instructions for the exercises are in the Assignments section.
    • Welcome to the course!

    Teaching material and contact persons

    The lectures will follow the notes provided at the following link: lecture notes; please contact Vanni Noferini for any issue relative to lectures or lecture notes.

    The material for example classes and homework will be posted by the head TA. Please contact Ryan Wood for any issue relative to example classes or homework.

    For administrative issues, for example failed registration in Sisu, please contact David Radnell (david dot radnell at aalto dot fi)

    Contacting the correct person (depending on which question you would like to ask) will likely result in a quicker response. Indeed, if for for example you contact Vanni Noferini for an administrative issue, your email will be forwarded to David Radnell anyway, but the additional step could result in a delayed answer.

    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 at the provided link 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.

    Exam information

    Please see the following link for

    (a) Individual study arrangements for exams (deadline to submit the form is 1 week before the exam, but the earlier the better)

    (b) Exam rooms (announced 1 or 2 days before the exam)