### 곽진호

포스텍 수학과 명예교수

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Linear Algebra

POSTECH
## 강좌 목차

## Instructor

### 곽진호

POSTECH

**교수**: 곽진호

**강좌 설명**

** **우리는 몇몇 응용분야에서 선형대수의 기본 개념을 배우고 있습니다. 본 강좌의 기본 개요는 매트릭스 및 결정인자, 벡터 공간, 선형 변환, 내부 제품 공간, 대각선화, 복합 매트릭스. 허용된 경우, 매트릭스의 여러 분해를 포함한 요르단 규약 양식에 대한 기본적 실천요강입니다.

**교재**

** **Jin Ho Kwak, Fundamentals of Linear Algebra(핵심선형대수학), 제2판, 경문사, 2020

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 |

포스텍 수학과 명예교수