Lecture schedule:

Date |
Topic |
Reading to prepare for class |
Quiz/Exam? |
Lecture Notes |

Tues, Jan 3 | Course overview; Systems of linear equations | Sections 1.1+1.2 | Scanned Notes | |

Thurs, Jan 5 | Row reduction and vector equations | Sections 1.2+1.3 | Scanned Notes | |

Tues, Jan 10 | Vectors and matrix equations | Sections 1.3+1.4 Some additional notes on vectors |
Quiz 1: Sections 1.1-1.3 |
Scanned Notes |

Thurs, Jan 12 | Matrix equations and solution sets | Sections 1.4+1.5 | Scanned Notes | |

Tues, Jan 17 | Applications of linear systems; linear independence | Sections 1.6+1.7 | Quiz 2: Sections 1.3-1.5 |
Scanned Notes |

Thurs, Jan 19 | Linear independence, linear transformations | Sections 1.7+1.8 | Scanned Notes | |

Tues, Jan 24 | Linear transformations, Matrix of a linear transformation | Sections 1.8+1.9 | Quiz 3: Sections 1.6-1.8 |
Scanned Notes |

Thurs, Jan 26 | Matrix of a linear transformation, and review | Section 1.9 | Scanned Notes | |

Tues, Jan 31 | Midterm 1: Sections 1.1-1.9 |
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Thurs, Feb 2 | Matrix operations | Section 2.1 | Scanned Notes | |

Tues, Feb 7 | Inverses of matrices | Section 2.2 | Quiz 4: Section 2.1 |
Scanned Notes |

Thurs, Feb 9 | Invertible matrices; subspaces of R^{n} |
Sections 2.3+2.5 | Scanned Notes | |

Tues, Feb 14 | Subspaces of R^{n}; dimension and rank |
Sections 2.5+2.6 | Quiz 5: Section 2.2-2.3 |
Scanned Notes |

Thurs, Feb 16 | Dimension and rank | Section 2.6 also coordinate system notes |
Scanned Notes | |

Tues, Feb 28 | Determinants | Section 3.1 | Quiz 6: Sections 2.5-2.6 |
Scanned Notes |

Thurs, Mar 2 | More about determinants | Section 3.2 | Scanned Notes | |

Tues, Mar 7 | Midterm 2: Sections 2.1-3.2 |
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Thurs, Mar 9 | Eigenvectors and eigenvalues | Section 4.1 | Scanned Notes | |

Tues, Mar 14 | The characteristic equation | Section 4.2 | Quiz 7: Section 4.1 |
Scanned Notes |

Thurs, Mar 16 | Eigenvectors and diagonalization | Section 4.3 Section 2 of coordinate system notes |
Scanned Notes | |

Tues, Mar 21 | Coordinate systems and diagonalization | Section 4.4 Section 2 of coordinate system notes |
Quiz 8: Sections 4.2-4.3 |
Scanned Notes |

Thurs, Mar 23 | Discrete Dynamical Systems | Section 4.6 Section 1 of dynamical systems notes |
Scanned Notes | |

Tues, Mar 28 | The inner product and orthogonality | Section 5.1 | Quiz 9: Sections 4.4 and 4.6 |
Scanned Notes |

Thurs, Mar 30 | Orthogonal sets, orthogonal projections | Sections 5.2, 5.3 | Scanned Notes | |

Tues, Apr 4 | Orthogonal projections, least squares | Sections 5.3, 5.5 | Quiz 10 |
Scanned Notes |

Thurs, Apr 6 | Least squares, the spectral theorem, and wrap-up | Section 5.5 | Scanned Notes |

The sections listed above are for the textbook for the course, the third custom UBC edition of

- 1.1 Systems of linear equations

- 1.2 Row reduction and echelon forms

- 1.3 Vector equations

- 1.4 The matrix equation Ax = b

- 1.5 Solution sets of linear equations

- 1.6 Applications of linear systems (skip chemical equations)

- 1.7 Linear independence

- 1.8 Introduction to linear transformations

- 1.9 The matrix of a linear transformation

- 2.1 Matrix operations

- 2.2 The inverse of a matrix (skip elementary matrices)

- 2.3 Characterizations of invertible matrices

- 2.5 Subspaces of Rn

- 2.6 Dimension and rank

- 3.1 Introduction to determinants

- 3.2 Properties of determinants

- 4.1 Eigenvectors and eigenvalues

- 4.2 The characteristic equation

- 4.3 Diagonalization

- 4.4 Eigenvectors and linear transformations

- 4.6 Discrete dynamical systems

- 5.1 Inner product, length, and orthogonality

- 5.2 Orthogonal sets

- 5.3 Orthogonal projections

- 5.5 Least-square problems