포스텍 수학과 명예교수
(1) Mr A Hui J (贾阿辉) firstname.lastname@example.org
(2) Mr Fu Gang Yin (尹富纲) email@example.com
Lecture (by Kwak)
Recitation by Teaching Assistant
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.
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)
Linear Algebra, Lecture note by J. Kwak (2019)
What is a matrix?
Products of matrices
Systems of Linear Equations, by a matrix!
The Determinant is a fuction
Existence and uniqueness of the determinant fuction
Further computing detA and Cramer's rule
Subspaces as Vector Spaces
Linear dependence Linear independence
Bases and Coodinate System
Row spaes, Column spaces and Null spaces
Change of bases
Inner Product Spaces
Geometry on an inner product space
Gram-Schmidt orthogonalization and Rectangular coordinate system
Orthogonal Projections, ProjU and Projection Matrix
Orthogonal matrices are isometries
Diagonalization of Matrices
Which matrices are diagonalizable?
Applications of the diagonalization
Complex Vector Spaces
Hermitian, Skew-Hermitian, and Unitary matrices
Orthogonally Diagonalizable Matrices and Unitarily Diagonalizable Matrices
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