Topic outline

  • MS-C1342 Linear Algebra

    • Period V: 19 April - 4 June 2021
    • Lecturer: Vanni Noferini, vanni dot noferini at aalto dot fi
    • Head assistants: Milo Orlich, milo dot olrich at aalto dot fi, and Ryan Wood, ryan dot wood at aalto dot fi
    • Registration at WebOodi
    • In 2020/21 the course is fully online and on Zoom. Instructions and links for the lectures can be foound in the Announcement sections; instructions and links 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.

    Final exam

    The final exam will be held online on Friday 4 June 2021. More detailed instructions will appear nearer the time.

    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.

    Exercise sessions and Zulip

    See the MyCourses Section "Assignments" for details about the exercise sessions on Zoom.

    There also is a Zulip chat for this course, which you can join at:
    https://ms-c1342.zulip.cs.aalto.fi/join/xuw8iz0ynszvts55qmdexa14/