# Linear algebra

## General information

##### Lecturer:

##### 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

Saturday 10h15--12h, room CM1104, CM1105, CM1106, and GCA331

##### Principal assistant:

#### Important Notes:

**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.**

## 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 (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) |