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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
學  分
3
             
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

Workload
l   PAPERHOMEWORK
l   TUTORIAL / PRESENTATION
l   MIDTERM
l   FINAL EXAM
好重
1

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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,major為數學系,不要選
評價教員教學
#1 長期面帶笑
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
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