Trinity College Dublin

Lecture | Topics covered | Notes |
---|---|---|

1 (27.09) | Introduction, vectors, vector addition, and dot products | Notes 1 |

2 (29.09) | Cross products, multilinearity, and areas or parallelograms | Notes 2 |

3 (30.09) | Lines and planes in three-dimensional space | Notes 3 |

4/5 (04.10,06.2026) | Systems of linear equations, reduced row echelon form/Gauss-Jordan elimination,linear combinations/span, column space | Notes 4/5 |

Tutorial 1 | Tutorial 1 | |

6 (11.10.2026) | Matrix operations: Matrix addition, scalar multiplication, and matrix multiplication | Notes 6 |

7 (13.10.2026) | Elementary matrices and Matrix Inverses | Notes 7 |

8 (14.10.2026) | Determinants and Permutations | Notes 8 |

9 (18.10.2026) | Determinants and invertibility, transposes, minors and cofactors | Notes 9 |

10 (20.10.2026) | Determinants by Laplace expansion and inverses by adjoint matrices | Notes 10 |

21.10.2016 | Tutorial 2 | Tutorial 2 |

11 (25.10.2016) | 3x3 determinants, vector spaces | Notes 11 |

12 (27.10.2016) | Properties of vector spaces and subspaces | Notes 12 |

13 (28.10.2016) | Direct sums of vector spaces and spans of vectors | Notes 13 |

14/15 (01/03.11.2016) | Linear Independence and Bases | Notes 14/15 |

(04.11.2016) | Tutorial 3 | Tutorial 3 |

16 (15.11.2016) | Dimensions and coordinates | Notes 16 |

17 (17.11.2016) | Linear transformations | Notes 17 |

18 (18.11.2016) | Injective and surjective functions and transformations | Notes 18 |

19 (22.11.2016) | Matrix representations of linear transformations | Notes 19 |

20 (24.11.2016) | Compositions of linear transformations and change of basis | Notes 20 |

(25.11.2016) | Tutorial 4 | Tutorial 4 |

(28.11.2016) | Review | Practice problems done in class |

(01.12.2016) | Further topics: Eigenvectors and eigenvalues | |

(02.12.2016) | Further topics: Diagonalization | |

(06.12.2016) | Application 1: A formula for Fibonacci numbers | |

(08.12.2016) | Application 2: A rough idea of how Google works | A detailed survey by David Austin |

(09.12.2016) | Tutorial 5 | Tutorial 5 |

(13.12.2016) | Review Day 1 | Practice Problems in class |

(15.12.2016) | Review Day 2 | Practice Problems in class |

(16.12.2016) | Review Day 3 | Practice Problems in class |