Sep 6 |
1.1, 1.2 |
Fields, vector spaces |

Sep 10 |
1.2–1.3 |
Properties of vector spaces, linear combinations |

Sep 13 |
1.4, 1.5 |
Linear combinations, subspaces |

Sep 17 |
1.5, 2.1 |
Direct sums, linear maps |

Sep 20 |
2.2, 2.3 |
Kernel and image, vector spaces of linear maps |

Sep 24 |
2.4, 3.1 |
Isomorphisms, spans |

Sep 27 |
3.2, 3.3 |
Linear dependence/independence, finitely generated vector spaces |

Oct 1 |
3.4 |
Basis and dimension |

Oct 4 |
3.4, 3.5 |
Basis and dimension, the Dimension Theorem |

Oct 11 |
3.5–3.7 |
The Dimension Theorem, dimensions of spaces of linear maps, dual spaces |

Oct 15 |
3.7, 4.1 |
Dual spaces, the matrix of a linear map |

Oct 18 |
4.1, 4.2 |
The matrix of a linear map, similar matrices |

Oct 22–26 |
Reading week |

Oct 29 |
4.3, 4.4 |
Gaussian elimination, the rank of a matrix |

Nov 1 |
5.1, 5.2 |
Multilinear maps, the determinant |

Nov 5 |
1.1–4.4 |
**Midterm test** |

Nov 8 |
5.3, 5.4 |
Properties of the determinant |

Nov 12 |
6.1 |
Inner product spaces |

Nov 15 |
6.2 |
Orthogonality |

Nov 19 |
6.3 |
Adjoints |

Nov 22 |
TBA |
Eigenvectors and eigenvalues |

Nov 26 |
TBA |
Diagonalization |

Nov 29 |
TBA |
Diagonalization of symmetric matrices |

Dec 3 |
TBA |
Diagonalization of symmetric matrices |

Dec 5 |
N/A |
Review |