Linear Algebra(EN)

POSTECH

수강신청

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)

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

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