# Linear algebra

## 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

Saturday 14h15 - 16h00, room GCA330, GCA331, (extra rooms will be assigned if necessary)

##### Principal assistant:

## Course

#### Book

- Linear Algebra and its Applications, D.C. Lay, Pearson (5th edition).

#### 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) |