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General information

Lecturer:

John H. Maddocks

Hours:

The course will be run as a flipped class. The weekly course material, videos, class notes, exercises, and solutions, will be made available online on Moodle with updates every Monday morning. Zoom links as an alternative to physical presence at the lectures and exercises are available on the Moodle page.

Lectures: Tuesday 21.9.2021 at 13h15 - 15h00, room CO2
      Each Thursday 14h15 - 16h00, room CE3

Exercises: Thursday 16h15 - 18h00, room CM1120, CM1121, (extra rooms will be assigned if necessary)
      Saturday 14h15 - 16h00, room GCA330, GCA331, (extra rooms will be assigned if necessary)

Principal assistant:

Harmeet Singh

Course

Book

  • Linear Algebra and its Applications, D.C. Lay, Pearson (5th edition).
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. Apparently there is a 6th edition of the book available now, but we haven't seen it yet.

Week-by-week correspondence

Week 1 (20.9) 0.0 - Introduction and Logistics, 1.1 - System of linear equations, 1.2 - Row reduction and echelon forms, 1.3 - Vector equations
Week 2 (27.9) 1.4 - The matrix equation, 1.5 - Solutions sets of linear systems
Week 3 (4.10) 1.7 - Linear independence, (1.8 - Introduction to linear transformations + 1.9 - The matrix of a linear transformation) start ...
Week 4 (11.10) ... end (1.8 - Introduction to linear transformations + 1.9 - The matrix of a linear transformation), 2.1 - Matrix operations
Week 5 (18.10) 2.2 - The inverse of a matrix, 2.3 - Characterizations of invertible matrices, 2.6 - Iterative methods and Neumann series (optional)
Week 6 (25.10) 2.5 - Matrix factorizations, 3.1 - Introduction to determinants
Week 7 (1.11) 3.2 - Properties of determinants, 3.3 - Cramer's rule, volume, and linear transformations, 4.1 - Vector spaces and subspaces
Week 8 (8.11) 4.2 - Null spaces, column spaces, and linear transformations, 4.3 - Linearly independent sets; bases
Week 9 (15.11) 4.4 - Coordinate systems, 4.5 - The dimension of a vector space, 4.6 - Rank
Week 10 (22.11) 4.7 - Change of basis, 5.1 - Eigenvectors and eigenvalues, 5.2 - The characteristic equation.
Week 11 (29.11) 5.3 - Diagonalization, 5.4 - Eigenvectors and linear transformations, 6.1 - Inner product, length, and orthogonality.
Week 12 (6.12) 6.2 - Orthogonal sets, 6.3 - Orthogonal projections, 6.4 - The Gram-Schmidt process
Week 13 (13.12) 6.5 - Least-Squares problems, 6.6 - Applications to linear models, 7.1 - Diagonalization of symmetric matrices
Week 14 (20.12)

Exercises

Exercises and solutions will be posted on Moodle.