# Linear algebra

## General information

##### Lecturer:

##### Hours:

Lectures: tuesday 13h15--15h, room CE6; thursday 14h15--16h, room CE6

Exercises: tuesday 15h15--16h, room CM1104, CM1105, CM1106, and GCA331(reserved but not used)

thursday 16h15--17h, room CM1120, CM1121, MAA110 (reserved but not used), and CM013 (reserved but not used)

##### Principal assistant:

## Course

#### Book

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

Note: 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 (16.9) |
1.1 - System of linear equations, 1.2 - Row reduction and echelon forms, 1.3 - Vector equations, 1.4 - The matrix equation.... |

Week 2 (23.9) |
....1.4 - The matrix equation, 1.5 - Solutions sets of linear systems, 1.7 - Linear independence, 1.8 - Introduction to linear transformations, 1.9 - The matrix of a linear transformation.... |

Week 3 (30.9) |
....1.9 - The matrix of a linear transformation, 2.1 - Matrix operations. |

Week 4 (7.10) |
2.1 - Matrix operations, 2.2 - The inverse of a matrix, 2.3 - Characterizations of invertible matrices.... |

Week 5 (14.10) |
....2.3 - Characterizations of invertible matrices, 3.1 - Introduction to determinants, 3.2 - Properties of determinants, 3.3 - Cramer's rule, volume, and linear transformations. |

Week 6 (21.10) |
4.1 - Vector spaces and subspaces, 4.2 - Null spaces, column spaces, and linear transformations, 4.3 - Linearly independent sets; bases. |

Week 7 (28.10) |
4.4 - Coordinate systems, 4.5 - The dimension of a vector space, 4.6 - Rank. |

Week 8 (4.11) |
4.7 - Change of basis, 5.1 - Eigenvectors and eigenvalues, 5.2 - The characteristic equation. |

Week 9 (11.11) |
5.3 - Diagonalization, 5.4 - Eigenvectors and linear transformations, 6.1 - Inner product, length, and orthogonality. |

Week 10 (18.11) |
6.2 - Orthogonal sets, 6.3 - Orthogonal projections. |

Week 11 (25.11) |
6.4 - The Gram-Schmidt process, 6.5 - Least-Squares problems. |

Week 12 (2.12) |
7.1 - Diagonalization of symmetric matrices (end of obligatory material), 7.2 - Quadratic forms, 7.3 - Rayleigh Quotients.... |

Week 13 (9.12) |
....7.3 - Rayleigh Quotients, 7.4 - The singular value decomposition, 2.4 - Partitioned matrices.... |

Week 14 (16.12) |
....2.4 - Partitioned matrices, 2.5 - Matrix factorizations, 5.5 - Complex eigenvalues. |