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

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

교수자

곽진호

포스텍 수학과 명예교수