1
课程详述
COURSE SPECIFICATION
以下课程信息可能根据实际课需要或在课程检讨之后产生变动。如对课程有任何疑问,
联系授课教师。
The course information as follows may be subject to change, either during the session because of unforeseen
circumstances, or following review of the course at the end of the session. Queries about the course should be
directed to the course instructor.
1.
课程名称 Course Title
线性代数 LINEAR ALGEBRA
2.
授课院系
Originating Department
数学系 Department of Mathematics
3.
课程编号
Course Code
MA113
4.
课程学分 Credit Value
4 学分 4 Credits
5.
课程类别
Course Type
通识必修课程 General Education (GE)Required Courses
6.
授课学期
Semester
春季 Spring / 秋季 Fall
7.
授课语言
Teaching Language
英文 English / 中英双语 English & Chinese
8.
他授课教师)
Instructor(s), Affiliation&
Contact
For team teaching, please list
all instructors
Yimao Chen
M5006, College of Science
Department of Mathematics
SUSTech
9.
验员/、所、联
方式
Tutor/TA(s), Contact
待公布 To be announced
10.
选课人数限额(可不)
Maximum Enrolment
Optional
2
11.
授课方式
Delivery Method
讲授
Lectures
实验/
Lab/Practical
其它(具体注明)
OtherPleasespecify
总学时
Total
学时数
Credit Hours
64
N/A
复习、考试1 周) 4
Revision & Exam (1
week) 4-hours
100
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
无/None
13.
后续课程、其它学习规划
Courses for which this
course is a pre-requisite
线
、回归分析、金融数学及金融工程等课程的先修课程,同时也是其他工程学
多门专业课的先修课程。
Linear Algebra is a prerequisite for Advanced Linear Algebra. It’s also a
prerequisite for many mathematics courses including Numerical analysis,
Ordinary differential equations, Partial differential equations, Regression
analysis, Financial Mathematics and Financial Engineering and etc.
14.
其它要求修读本课程的学系
Cross-listing Dept.
教学大纲及教学日历 SYLLABUS
15.
教学目标 Course Objectives
本课程的教学目的是培养学生严谨的逻辑推理和抽象思维能力。课程主要讲述线性代数基本的概念和理论,
包括线性方程组、矩阵代数、行列式、向量空间、线性变换、正交性理论、特征值和特征向量、奇异值分解
以及二次型等相关理论,为进一步学习线性代数精讲的内容打下坚实的基础。课程的重点包括矩阵运算、求
解线性方程组、向量空间、线性变换的相关理论求解特征值和特征向量以及二次型。
To introduce the basic concepts in linear algebra including systems of linear equations, matrix algebra,
determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, singular value
decomposition and quadratic forms. It is a prerequisite for Advanced Linear Algebra. The emphasis is on
operations with matrices, solving systems of linear equations, fundamental theory of vector spaces and
linear transformations, solving eigenvalues and eigenvectors problems, and quadratic forms.
16.
预达学习成果 Learning Outcomes
通过对本课程的学习,学生可以理解和掌握线性代数的基本理论和技巧,能够熟练掌握行列式的基本理论和求
方法;熟练掌握矩阵的基本算和矩阵的逆;熟练掌握求解线性方程组的方法;熟练掌握矩阵特征值和特
向量计算;熟掌握斯密(Schmidt)正交法;理解量线相关的理n 实空的基和正
基、相似矩阵及矩阵可对角化、二次型的基本理论以及线性变换。
After completing this course, students should understand the basic methods and techniques in Linear
Algebra. They should be able to compute determinants, manipulate matrices and do matrix algebra, solve
systems of linear equations, compute eigenvalues and eigenvectors. After learning this course, students
should be able to understand the basic concepts of linear independence and linear dependence, the basis
and orthonormal basis of n-dimensional vector space, similar matrices and diagonalizable matrices,
quadratic forms and linear transformations.
3
17.
课程内容及教学日历 (如授课语言以英文为主,则课程内容介绍可以用英文;如团队教学或模块教学,教学日历须注明
主讲人)
Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if
this is a team teaching or module course.)
Week 1:
1.1 Introduction
1.2 The geometry of Linear Equations
1.3 An example of Gaussian Elimination
1.4 Matrix Notation and Matrix Multiplication
1.1 简介
1.2
线性方程的几何理解
1.3 高斯消元
1.4
矩阵介绍和矩阵乘法
Week 2:
1.4 Matrix Notation and Matrix Multiplication
1.5 Triangular Factors and Row Exchanges
1.6 Inverses and Transposes
1.4
矩阵记号和矩阵乘法
1.5 矩阵的三角分解和行交换
1.6
矩阵的逆和转置
Week 3:
1.6 Inverses and Transposes
2.1 Vector spaces and subspaces
1.6 矩阵的逆和转置
2.1 向量空间和子空间
Week 4
2.2 Solving Ax=0 and Ax=b
4
2.2 求解 Ax=0 Ax=b
Week 5:
2.3. Linear Independence, Basis, and Dimension
2.4 The Four Fundamental Subspaces
2.3.
线性无关性,基,维数
2.4 矩阵的四个基本子空间
Week 6:
2.6 Linear Transformations
2.6
线性变换
Week 7:
3.1 Orthogonal Vectors and Subspaces
3.2 Cosines and Projections onto Lines
3.3 Projections and Least Squares
3.1
正交向量和正交子空间
3.2 投影到直线
3.3
投影和最小二乘
Week 8:
3.3 Projections and Least Squares--cont’d
3.4 Orthogonal Bases and Gram Schmidt
3.3 投影和最小二乘
3.4 正交基和施密特正交化
Week 9:
4.1 Introduction
4.2 Properties of The Determinant
4.3 Formulas for the Determinant