### 곽진호

포스텍 수학과 명예교수

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Linear Algebra(EN)

POSTECH
## 강좌 목차

## Instructor

### 곽진호

POSTECH

**Lecturer**: Prof. Jin Ho Kwak(郭振鎬)**TA: Teaching Assistant**:

(1) Mr A Hui J (贾阿辉) __18121577@bjtu.edu.cn__

(2) Mr Fu Gang Yin (尹富纲) __18118010@bjtu.edu.cn__

** **

- Credits/Lecture hour: 56 sessions (50 mins/session)+ Recitations, with 3 credits

**Lecture (by Kwak)**

- Tuesday 10:10~12:00 AM (1-14th Weeks) at East Campus Building, DQ110
- Thursday 8:00~ 9:50 AM (1-14th Weeks) at East Campus Building, DQ110

**Recitation by Teaching Assistant**

**Every**Wednesday from Sept 18, 7:00~8:50 PM at Main Campus (YF208).

**Course Description**

** **We are learning a basic concept of linear algebra with some applications. The basic synopsis of this course are basic properties of Matrices and Determinants, Vector spaces, linear transformations, Inner product spaces, Diagonalizations, Complex matrices, If allowed, elementary practice for Jordan Canonical forms including several decompositions of matrices. THE CLASS WILL BE TAUGHT IN ENGLISH.

**Prerequisite/Requirement**

** **

No special prerequisite beyond the basic algebra in high-school level. There should be no absence in class since preparations and reviews are important to go through this course successfully. Without a prior approval, more than FIVE times of absence in class will make F grade unless a student withdraws it. Quiz, about 10-15 minutes exam., will come up in class without any early notice.

**Course Evaluation Criteria**

** **

Midterm Exam I (100 minutes) 25% will be held on **Oct 8 (Tuesday)**

Midterm Exam II (100 minutes) 25% will be held on **Nov 26 (Tuesday)**

- Final Exam (120 minutes) 30% (To be announced later);
- Quizzes, Homework, Attending the class, etc 20%

**Textbook**

** ****Linear Algebra, Lecture note by J. Kwak (2019)**

강의개요 | |

Week 1 | What is a matrix? |

Products of matrices | |

Week 2 | Systems of Linear Equations, by a matrix! |

Elementary matrices | |

Week 3 | Invertible matrices |

The Determinant is a fuction | |

Week 4 | Existence and uniqueness of the determinant fuction |

Further computing detA and Cramer's rule | |

Week 5 | Spaces |

Subspaces as Vector Spaces | |

Week 6 | Linear dependence Linear independence |

Bases and Coodinate System | |

Week 7 | Row spaes, Column spaces and Null spaces |

Linear Transformations | |

Week 8 | Change of bases |

Inner Product Spaces | |

Week 9 | Geometry on an inner product space |

Gram-Schmidt orthogonalization and Rectangular coordinate system | |

Week 10 | Orthogonal Projections, ProjU and Projection Matrix |

Orthogonal matrices are isometries | |

Week 11 | Diagonalization of Matrices |

Which matrices are diagonalizable? | |

Week 12 | Applications of the diagonalization |

Complex Vector Spaces | |

Week 13 | Hermitian, Skew-Hermitian, and Unitary matrices |

Orthogonally Diagonalizable Matrices and Unitarily Diagonalizable Matrices | |

Week 14 | Jordan Canonical Forms(JCF) |

GIVEN A, HOW TO FIND JCF J AND A CHANGE OF BASIS MATRIX Q IN THE Jordan decomposition A = QJQ-1? | |

The powers Jk and Ak Cayley-Hamilton Theorem |

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