You can find the syllabus here.

Week | Subjects to be covered |
---|---|

1 | The geometry of linear equations (1.1, 1.2), Gaussian eliminations (1.3) |

2 | Matrices, operations on matrices, (1.4) |

3 | Row operations (1.5), Invertibility, inverse and transpose of a matrix, (1.6) |

4 | Vector spaces and subspaces (2.1), Solving homogeneous and non-homogeneous systems (2.2) |

5 | Linear independence, basis, and dimension (2.3) |

6 | The four fundamental subspaces (2.4), Linear transformations (2.6) |

7 | Orthogonal vectors and subspaces, inner products (3.1) |

8 | Projections, Orthogonal bases and Gram-Schmidt (3.2,3.3,3.4) |

9 | Determinants: definition, properties (4.1, 4.2) |

10 | Formulas for determinant (4.3) and applications of determinant (4.4) |

11 | Eigenvalues and eigenvectors (5.1) |

12 | Diagonalization (5.2) |

13 | Power of a matrix and Matrix exponentials (5.3, 5.4) |

14 | Similarity Transformations (5.6) |