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Linear algebra

General information

This is the 2020-21 version of the page. The new page is here .

Lecturer:

John H. Maddocks

Hours:

The lectures will all be pre-recorded and made available online on Moodle. Nevertheless, the following rooms are reserved for your use on the days you are allowed on campus.

Lectures: Tuesday 13h15--15h, room CO2; Thursday 14h15--16h, room CE3

Exercises: Thursday 16h15--18h, room CM1120, CM1121 (reserved but not used), CM013 (reserved but not used), MAA110 (reserved but not used);
      Saturday 10h15--12h, room CM1104, CM1105, CM1106, and GCA331

Principal assistant:

Harmeet Singh

Important Notes:

  • The course will be conducted online, i.e. all the lectures will be pre-recorded and the videos will be made available to the students on Moodle at the beginning of each week.
  • Starting on 9 September, students must use the following Moodle page to enrol for the course. This will allow them to view all the information they need for the class, and receive important communications regarding the course by e-mail . The students must subsequently register for the course on IS-Academia between 14 September and 25 September. Failing to do so, they will be automatically removed from the Moodle list.
  • If you have any difficulty registering for the course on Moodle, or for any other questions regarding the logistics of the course, please contact the principle assistant Harmeet Singh by e-mail.

    • Course

    Book

    • Linear Algebra and its Applications, D.C. Lay, Pearson (5th edition).
    Week by week schedule of the sections of the book to be covered will be provided below as the course progresses.

    Note: All students are required to have access to a recent edition of the D.C. Lay book mentioned above. The course will follow the precise numbering of the 5th edition (which is not very different from the 4th). Any other edition would also suffice. In case of discrepancy, follow the topics by title.

    Week-by-week correspondence

    Week 1 (14.9) 0.0 - Introduction and Logistics, 1.1 - System of linear equations, 1.2 - Row reduction and echelon forms, 1.3 - Vector equations
    Week 2 (21.9) 1.4 - The matrix equation, 1.5 - Solutions sets of linear systems
    Week 3 (28.9) 1.7 - Linear independence, (1.8 - Introduction to linear transformations + 1.9 - The matrix of a linear transformation)....
    Week 4 (5.10) ....(1.8 - Introduction to linear transformations + 1.9 - The matrix of a linear transformation), 2.1 - Matrix operations
    Week 5 (12.10) 2.2 - The inverse of a matrix, 2.3 - Characterizations of invertible matrices, 2.6 - Iterative methods and Neumann series (optional)
    Week 6 (19.10) 2.5 - Matrix factorizations, 3.1 - Introduction to determinants
    Week 7 (26.10) 3.2 - Properties of determinants, 3.3 - Cramer's rule, volume, and linear transformations, 4.1 - Vector spaces and subspaces
    Week 8 (2.11) 4.2 - Null spaces, column spaces, and linear transformations, 4.3 - Linearly independent sets; bases
    Week 9 (9.11) 4.4 - Coordinate systems, 4.5 - The dimension of a vector space, 4.6 - Rank
    Week 10 (16.11) 4.7 - Change of basis, 5.1 - Eigenvectors and eigenvalues, 5.2 - The characteristic equation.
    Week 11 (23.11) 5.3 - Diagonalization, 5.4 - Eigenvectors and linear transformations, 6.1 - Inner product, length, and orthogonality.
    Week 12 (30.11) 6.2 - Orthogonal sets, 6.3 - Orthogonal projections, 6.4 - The Gram-Schmidt process
    Week 13 (7.12) 6.5 - Least-Squares problems, 6.6 - Applications to linear models, 7.1 - Diagonalization of symmetric matrices (end of obligatory material)
    Week 14 (14.12)

    Exercises

    Exercises and solutions will be posted on Moodle.