## General information

##### 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 Saturday evening of the previous week. 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 - 15h30, room GCA330, GCA331, (extra rooms will be assigned if necessary)

## 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.

#### 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 Week 6 (25.10) 2.4 - Partitioned matrices (partial), 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 (Note: In the 6th edition, this section has been eliminated and all of the material is merged into sections 4.3 and 4.5) Week 10 (22.11) 4.7 - Change of basis (Note: In the 6th edition, this section is numbered 4.6), 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 (Note: This section has been renamed to "Machine learning and linear models" in the 6th edition), 7.1 - Diagonalization of symmetric matrices Week 14 (20.12) 7.2 Quadratic forms, 7.3 Constrained optimization (with focus on Rayleigh Quotients), 7.4 The singular value decomposition

## Exercises

Exercises and solutions will be posted on Moodle.