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Linear Algebra


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


강좌 목차


의개요
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


Instructor

곽진호

포스텍 수학과 명예교수


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