Linear algebra is an algebraic and geometric theory of properties called linearity. In Linear Algebra 1, we focused on algebraic
properties and learned about them.

In this class, students learn about linear algebra from a geometric standpoint, including vector spaces and linear mappings.

In this class, students learn about linear algebra from a geometric standpoint, including vector spaces and linear mappings.

The purpose of this class is to understand the geometric meaning of the content learned in Linear Algebra 1 and to be able
to calculate it.

- To be able to verify the basic properties of numerical vector spaces with concrete examples.
- To be able to verify the basic properties of vector spaces with concrete examples.
- To be able to verify the basic properties of linear mappings with concrete examples.
- To be able to verify the basic properties of metric vector spaces with concrete examples.
- To be able to verify the geometric meaning of linear and affine transformations with concrete examples.

Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
---|---|---|---|

1. | Numerical vector space, inner product and outer product | Read through the textbook p.83-p.93 and handouts, and solve the exercises before class. Review after class. | 190minutes |

2. | Line, plane and quadratic curve | Read through the textbook p.93-p.101 and handouts, and solve the exercises before class. Review after class. | 190minutes |

3. | Vector space and linear independence | Read through the textbook p.103-p.117 and handouts, and solve the exercises before class. Review after class. | 190minutes |

4. | Basis and dimension | Read through the textbook p.117-p.126 and handouts, and solve the exercises before class. Review after class. | 190minutes |

5. | Linear mapping and linear isomorphism | Read through the textbook p.129-p.136 and handouts, and solve the exercises before class. Review after class. | 190minutes |

6. | Matrix representation of linear mapping, composite mapping and inverse mapping | Read through the textbook p.137-p.148 and handouts, and solve the exercises before class. Review after class. | 190minutes |

7. | Midterm examination and its explanation | Preparation of midterm examination. | 190minutes |

8. | Inner product and orthonormal basis | Read through the textbook p.171-p.179 and handouts, and solve the exercises before class. Review after class. | 190minutes |

9. | Orthogonal transformation and diagonalization of symmetric matrix | Read through the textbook p.179-p.187 and handouts, and solve the exercises before class. Review after class. | 190minutes |

10. | Quadratic form | Read through the textbook p188-p.193 and handouts, and solve the exercises before class. Review after class. | 190minutes |

11. | Geometric meaning of linear transformations 1 | Read through the textbook p.197-p.205 and handouts, and solve the exercises before class. Review after class. | 190minutes |

12. | Geometric meaning of linear transformations 2 | Read through the textbook p.205-p.210 and handouts, and solve the exercises before class. Review after class. | 190minutes |

13. | Affine transformation and its geometric meaning | Read through the textbook p.148-p.153, p.211-p.212 and handouts, and solve the exercises before class. Review after class. | 190minutes |

14. | Final examination and its explanation | Preparation of final examination. | 190minutes |

Total. | - | - | 2660minutes |

Midterm examination | Final examination | Reports and little examinations | Total. | |
---|---|---|---|---|

1. | 10% | 7% | 17% | |

2. | 10% | 7% | 17% | |

3. | 10% | 6% | 16% | |

4. | 15% | 10% | 25% | |

5. | 15% | 10% | 25% | |

Total. | 30% | 30% | 40% | - |

Midterm examination(30%), Final examination(30%), Reports and little examinations(40%)

60% if students can understand and solve exercises in the handouts

60% if students can understand and solve exercises in the handouts

- Course that cultivates an ability for utilizing knowledge

Work experience | Work experience and relevance to the course content if applicable |
---|---|

N/A | 該当しない |

Last modified : Sun Sep 04 04:03:20 JST 2022