1
课程详述
COURSE SPECIFICATION
以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问，请
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.
授课教师、所属学系、联系方
式（如属团队授课，请列明其
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.
实验员/助教、所属学系、联系
方式
Tutor/TA(s), Contact
待公布 To be announced
10.
选课人数限额(可不填)
Maximum Enrolment
（Optional）
2
11.
授课方式
Delivery Method
讲授
Lectures
实验/实习
Lab/Practical
其它(请具体注明)
Other（Pleasespecify）
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
后续课程为线性代数精讲，是金融数学系的数值分析、常微分方程、偏微分方
程、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科
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
解方法；熟练掌握矩阵的基本运算和矩阵的逆；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
征向量的计算；熟练掌握斯密特(Schmidt)正交化方法；理解向量线性相关性的理论、n 维实空间的基和正交
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 和 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 投影到直线上
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
5
4.1 行列式简介
4.2 行列式的基本性质
4.3
行列式的计算
Week 10:
4.3 Formulas for the Determinant--cont’d
4.4 Applications of Determinants
4.3 行列式的计算
4.4
行列式的应用
Week 11:
5.1 Introduction
5.2 Diagonalization of a Matrix
5.1 特征值简介
5.2 矩阵的对角化
Week 12:
5.5 Complex Matrices
5.6 Similarity Transformations
5.5 复数矩阵
5.6
相似变换
Week 13:
5.6 Similarity Transformations--cont’d
6.1 Minima, Maxima, and Saddle Points
5.6 相似变换
6.1 极小值、极大值以及鞍点
Week 14:
6.2 Test for Positive Definiteness (Quadratic Forms)
6.2 正定性的判定(二次型)
Week 15:
6.3 Singular Value Decomposition
6.3
奇异值分解
6
Week 16:
6.4 Minimum Principles
Review
6.4
极小值原理
总复习
18.
教材及其它参考资料 Textbook and Supplementary Readings
教材（Textbook）: Linear Algebra and Its Applications, 4
th
Edition, Gilbert Strang.
推荐参考书（Supplementary Readings）:
1. Linear Algebra with Applications, 9
th
Edition, Steven J. Leon.
2. 高等代数，北京大学数学系前代数小组编，第 4 版，高等教育出版社，2013.
课程评估 ASSESSMENT
19.
评估形式
Type of
Assessment
评估时间
Time
占考试总成绩百分比
% of final
score
违纪处罚
Penalty
备注
Notes
出勤 Attendance
5
课堂表现
Class
Performance
小测验
Quiz
15
课程项目 Projects
平时作业
Assignments
10
期中考试
Mid-Term Test
30
期末考试
Final Exam
40
期末报告
Final
Presentation
其它（可根据需要
改写以上评估方
式）
Others (The
above may be
modified as
necessary)
20.
记分方式 GRADING SYSTEM
A. 十三级等级制 Letter Grading
B. 二级记分制（通过/不通过） Pass/Fail Grading
7
课程审批 REVIEW AND APPROVAL
21.
本课程设置已经过以下责任人/委员会审议通过
This Course has been approved by the following person or committee of authority