MATH 2040 線性代數（二） Linear Algebra II

Course Code	MATH 2040 MATH2040			科目名稱		線性代數（二） Linear Algebra II
教員	Professor LI Man Chun [官方介紹] [學術著作]			學　　分		3學分
課程性質	數學系必修/ Mathematics and Information Engineering必修/數學教育必修			同科其他選擇
Workload	l   非PAPER類HOMEWORK l   TUTORIAL / PRESENTATION l   MIDTERM l   FINAL EXAM								好重	1
									重
									平均
									輕
									極輕
評價教學內容	#1 過深，一般數學系學生也未必明白。適合對數學有深入認識的同學，非major為數學系，不要選讀
評價教員教學	#1 長期面帶笑容
CUSIS科目資料	Description： This is a continuation of MATH1030. Topics include: linear transformations, matrix representation, nullity and rank; diagonalization, Cayley-Hamilton theorem; inner product spaces, normal and self-adjoint operators, quadratic forms; dual space, canonical forms, spectral theorem. Learning Outcome： We expect students to understand more advanced topics in linear algebra: eigenvalues and eigenvectors, canonical forms of matrices and linear transformations, inner product spaces, and bilinear and quadratic forms. - Students learn the idea of eigenvalues and eigenvectors and use them to diagonalize matrices. Students learn to find matrix limit and to study Markov process. - Students learn the structure of inner product spaces and orthogonal projection. Students learn to use the knowledge to find least squares approximation and minimal solutions. - Students learn how to orthogonally diagonalize a matrix or a linear transformation in an inner product space. - Students learn bilinear forms and quadratic forms. They know how to reduce a quadratic form to a canonical form and apply the knowledge to understand problems in finding maximum or minimal for a function of several variables. - Students learn how to obtain Jordan canonical form of a matrix over complex field. Students may learn how to apply this to solving ordinary differential equations.
其他資料	2017Sem1：學位 50|註冊 46|剩餘 4
同學推薦	高度推薦		推薦			有保留	1	極有保留