The schedule is tentative.

- Topic 1. Systems of linear equations.
- Topic 2. Matrices and vectors.
- Topic 3. Solution sets
- Topic 4. Nonsingularity.
- Topic 5. Linear combinations.
- Topic 6. Basis and dimension.
- Topic 7. Eigenvalues, eigenvectors and determinants.
- Everything in the previous topics will be assumed, and used freely where necessary.
- Topic 8. Inner-product.
- Everything in the previous topics will be assumed, and used freely where necessary.

Topic | Handout | Title | Schedule | Sequel to something? | Supplementary material | ||
---|---|---|---|---|---|---|---|

1 | 1 | What is solving a system of linear equations? | Notes | Week 1 Tuesday | |||

1 | 2 | Basic terminologies on systems of linear equations. | Notes | Week 1 Tuesday | |||

1 | 3 | Row operations on matrices. | Notes | Annotated Plates | Week 1 Thursday | ||

1 | 4 | Augmented matrix representation. | Notes | Week 2 Tuesday | 1.1, 1.2, 1.3. | ||

1 | 5 | Row-echelon forms and reduced row-echelon forms. | Notes | Annotated Plates | Week 2 Tuesday | 1.4. | |

1 | 6 | Classification of systems of linear equations in terms of reduced row-echelon forms. | Notes | Week 2 Tuesday | 1.5. |

Topic | Handout | Title | Schedule | Sequel to something? | Supplementary material | ||
---|---|---|---|---|---|---|---|

2 | 1 | Addition and scalar multiplication for matrices and vectors. | Notes | Week 2 Thursday | |||

2 | 2 | Matrix multiplication. | Notes | Annotated Plates | Week 3 Tuesday | 2.1. | |

2 | 3 | Vector presentation and matrix presentation for a system of linear equations and its solutions. | Notes | Week 3 Tuesday | 2.2. | ||

2 | 4 | Row operations and matrix multiplication. | Notes | Annotated Plates | Week 3 Tuesday | 1.3, 2.2. | |

2 | 5 | Miscellanies on matrices. | Notes | Annotated Plates | Week 3 Thursday | 2.1, 2.2. | |

2 | 6 | Examples of simple proofs in linear algebra. | Notes | Annotated Plates | Week 4 Tuesday | 2.5. | |

2 | 7 | Further miscellanies on mathematical reasoning in linear algebra. | Notes | Self-study supplementary material | 2.5, 2.6. |

Topic | Handout | Title | Schedule | Sequel to something? | Supplementary material | ||
---|---|---|---|---|---|---|---|

3 | 1 | Set notations in linear algebra. | Notes | Annotated Plates | Week 4 Tuesday | 1.1, 2.3. | |

3 | 2 | Homogeneous systems and null spaces. | Notes | Annotated Plates | Week 4 Tuesday | 3.1. | |

3 | 3 | Homogeneous system associated to a system of linear equations. | Notes | Annotated Plates | Week 4 Thursday | 3.1, 3.2. | |

3 | 4 | Geometry of solution sets for systems of linear equations. | Notes | Self-study supplementary material | 3.1. |

Topic | Handout | Title | Schedule | Sequel to something? | Supplementary material | ||
---|---|---|---|---|---|---|---|

4 | 1 | Non-singular matrices. | Notes | Annotated Plates | Week 5 Thursday | 3.2. | |

4 | 2 | Non-singularity in terms of row operations and matrix multiplication. | Notes | Annotated Plates | Week 6 Tuesday | 4.1. | |

4 | 3 | Non-singularity and invertibility. | Notes | Annotated Plates | Week 6 Tuesday | 4.2. | |

4 | 4 | Determining invertibility and computing matrix inverse through row operations. | Notes | Annotated Plates | Week 6 Tuesday | 4.3. | |

4 | 5 | Existence and uniqueness of solutions for a system of linear equations whose coefficient matrix is a square matrix. | Notes | Annotated Plates | Week 6 Thursday | 4.4. | |

4 | 6 | Row equivalence in terms of multiplication by non-singular and invertible matrices. | Notes | Annotated Plates | Week 6 Thursday | 4.4. |

Topic | Handout | Title | Schedule | Sequel to something? | Supplementary material | ||
---|---|---|---|---|---|---|---|

5 | 1 | Linear combinations. | Notes | Annotated Plates | Week 7 Tuesday | 2.1, 2.2, 4.3. | |

5 | 2 | Span of vectors and column space of a matrix. | Notes | Annotated Plates | Week 7 Tuesday | 3.1, 5.1. | |

5 | 3 | Subspaces of R^{n}. |
Notes | Annotated Plates | Week 7 Tuesday | 3.2, 5.2. | |

5 | 4 | Subspaces of R^{n} in contrast general subsets of R^{n}. |
Notes | Annotated Plates | Week 7 Thursday | 5.3. | |

5 | 5 | How to determine whether a given vector is the linear combination of some other vectors. | Notes | Annotated Plates | Week 8 Tuesday | 1.5, 1.6, 5.1. | |

5 | 6 | Linear dependence and linear independence. | Notes | Annotated Plates | Week 8 Tuesday | 3.2, 5.1. | |

5 | 7 | Theoretical results on linear dependence and linear independence. | Notes | Annotated Plates | Week 8 Tuesday | 4.3, 5.6. | |

5 | 8 | Theoretical results on span of vectors and column space of a matrix. | Notes | Annotated Plates | Week 8 Thursday | 4.3, 5.2. | |

5 | 9 | How to express the column space of a matrix as the null space of some matrix. | Notes | Self-study supplementary material | 1.6, 2.2, 3.2, 4.6, 5.2. |

Topic | Handout | Title | Schedule | Sequel to something? | Supplementary material | ||
---|---|---|---|---|---|---|---|

6 | 1 | Bases for subspaces of R^{n}. |
Notes | Annotated Plates | Week 9 Tuesday | 5.1, 5.2, 5.3, 5.6, 5.7. | |

6 | 2 | Gaussian elimination and basis for null space. | Notes | Annotated Plates | Week 9 Tuesday | 1.5, 3.2, 6.1. | |

6 | 3 | Minimal spanning sets. | Notes | Annotated Plates | Week 9 Tuesday | 5.1, 5.7, 5.8, 6.1. | |

6 | 4 | More on minimal spanning sets. | Notes | Annotated Plates | Week 9 Thursday | 6.3. | |

6 | 4A | Replacement Theorem (as Appendix to `More on minimal spanning sets'). | Notes | Self-study supplementary material | 5.7, 5.8, 6.1. | ||

6 | 5 | How to obtain a basis for the intersection of two subspaces of R^{n}. |
Notes | Self-study supplementary material | 5.9, 6.2. | ||

6 | 6 | Transpose and row space. | Notes | Annotated Plates | Week 9 Tuesday | 4.3, 5.8, 6.1. | |

6 | 6A | Duality between spanning and linear independence (as Appendix to `Transpose and row space'). | Notes | Self-study supplementary material | 6.6. | ||

6 | 7 | Dimension. | Notes | Week 10 Tuesday | 6.1, 6.4. | ||

6 | 8 | Inequalities on dimension. | Notes | Annotated Plates | Week 10 Tuesday | 6.4, 6.7. | |

6 | 8A | How to check whether some given vectors constitute a basis for a given subspace of R^{n} (as Appendix to `Inequalities on dimension'). |
Notes | Self-study supplementary material | 5.6, 6.3, 6.8. | ||

6 | 9 | Rank-nullity Formula. | Notes | Annotated Plates | Week 10 Tuesday | 6.2, 6.3, 6.6, 6.7, 6.8. | |

6 | 9A | Dimension relation on sum and intersection (as Appendix to `Rank-nullity Formula'). | Notes | Self-study supplementary material | 6.4, 6.7, 6.8, 6.9. | ||

6 | 9B | How bases for the same subspace of R^{n} relate to each other
(as Appendix to `Rank-nullity Formula'). |
Notes | Self-study supplementary material | 6.1, 6.7, 6.9. |

Topic | Handout | Title | Schedule | Sequel to something? | Supplementary material | ||
---|---|---|---|---|---|---|---|

7 | 1 | Eigenvalue and eigenvector. | Notes | Annotated Plates | Week 10 Thursday | ||

7 | 2 | Diagonalizability. | Notes | Annotated Plates | Week 11 Tuesday | 7.1. | |

7 | 3 | Determinants. | Notes | Annotated Plates | Week 11 Thursday | ||

7 | 4 | Multilinearity and Alternating property. | Notes | Annotated Plates | Week 12 Tuesday | 7.3. | |

7 | 5 | Products of determinants. | Notes | Annotated Plates | Week 12 Tuesday | 7.4. | |

7 | 6 | Characteristic polynomial of a matrix. | Notes | Annotated Plates | Week 12 Tuesday | 7.5. | |

7 | 7 | Adjoint of a matrix. | Notes | Self-study supplementary material | 7.5. |

Topic | Handout | Title | Schedule | Sequel to something? | Supplementary material | ||
---|---|---|---|---|---|---|---|

8 | 1 | Inner product, norm, and orthogonality. | Notes | Annotated Plates | Week 13 Tuesday | ||

8 | 2 | Orthogonal complement. | Notes | Self-study supplementary material | 8.1. | ||

8 | 3 | Orthonormal bases and orthogonal projections. | Notes | Annotated Plates | Week 13 Tuesday | 8.1, 8.2. | |

8 | 4 | Gram-Schmidt orthogonalization process. | Notes | Annotated Plates | Week 13 Thursday | 8.3. | |

8 | 5 | Orthogonal matrices. | Notes | Self-study supplementary material | 8.4. |