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 B Linear Algebra B
2.
授课院系
Originating Department
数学系 Department of Mathematics
3.
课程编号
Course Code
MA107B
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）
陈懿茂
数学系
慧园 3 栋 508
huy@sustech.edu.cn
Chen Yi mao
Department of Mathematics
Block 3, Room508, Wisdom Valley
Chenym@sustech.edu.cn
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
习题/辅导/讨论
Tutorials
实验/实习
Lab/Practical
其它(请具体注明)
Other（Please specify）
总学时
Total
学时数
Credit Hours
32
96
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
线性代数为数值分析、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 many mathematics curriculums 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在培养与其专业需求相关的应用和计算能力。讲述线性代数基本的概念和理论，包括行列式、矩阵、
向量和向量空间、线性方程组、矩阵的特征值和特征向量以及二次型。建议在习题课上向学生讲授如何使用 MATLAB 等
软件进行矩阵的运算和求解线性方程组。本课程的重点包括行列式的计算、矩阵运算、求解线性方程组以及求解特征值和
特征向量。
To introduce the basic concepts in linear algebra including determinants, matrices, vector spaces and systems of linear
equations, eigenvalues and eigenvectors of matrices, and quadratic forms. In tutorials, let students use MATLAB
performing matrices computation and solving systems of linear equations. The emphasis is on computation of
determinants, operations with matrices, solving systems of linear equations, and solving eigenvalues and eigenvectors
problems.
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；熟练掌握化二次形为标准形的方法；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、以及二次型的基本理论。
After completing this course, students should understand a few basic methods and techniques in Linear algebra. They
should be able to manipulate and compute determinants, manipulate matrices and do matrix algebra, solve systems of
linear equations, compute eigenvalues and eigenvectors and find the canonical form of a quadratic form. After learning
this course, students should also need to understand linear independence and linear dependence, the basis and
orthonormal basis of n-dimensional vector space, similar matrices and diagonalizable matrices and quadratic forms.
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.)
3
Week 1:
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equations Ax=b
第一周：
1.1 线性方程组
1.2 行化简和阶梯型
1.3 向量方程
1.4 矩阵方程 AX=b
Week 2:
1.5 Solution Sets of Linear Systems
1.7 Linear Independence
第二周：
1.5 线性方程组的解集合
1.7 线性无关性
Week 3:
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
第三周：
1.8 线性变换简介
1.9 线性变换的矩阵
Week 4:
2.1 Matrix Operations
2.2 The Inverse of a Matrix
第四周：
2.1 矩阵运算
4
2.2 矩阵的逆
Week 5:
2.3 Characterizations of Invertible Matrices
2.4 Partitioned Matrices
2.5 Matrix Factorizations
第五周：
2.3 可逆矩阵的刻画
2.4 矩阵分块
2.5 矩阵分解
Week 6:
2.8 Subspaces of Rn
2.9 Dimension and Rank
第六周：
2.8 Rn 的子空间
2.9 维数和秩
Week 7:
3.1 Introduction to Determinants
3.2 Properties of Determinants
第七周：
3.1 行列式简介
3.2 行列式的性质
Week 8:
3.3 Cramers’s Rule, Volume, and Linear Transformations
第八周：
3.3 克莱姆法则、体积和线性变换
Week 9:
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
5
第九周：
4.1 向量空间和子空间
4.2 零空间、列空间和线性变换
Week 10:
4.3 Linearly independent Sets; Bases
4.5 The Dimension of a Vector Space
第十周：
4.3 线性无关集；基
4.4 向量空间的维数
Week 11:
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
第十一周：
5.1 特征向量和特征值
5.2 特征方程
Week 12:
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
第十二周：
5.3 对角化
5.4 特征向量和线性变换
Week 13
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
第十三周：
6.1 内积、长度和正交性
6.2 正交集
6
Week 14:
6.3 Orthogonal Projections
6.4 The Gram-Schmidt Process
第十四周：
6.3 正交投影
6.4 Gram-Schmidt 正交化过程
Week 15:
7.1 Diagonalization of Symmetric Matrices
7.2 Quadratic Forms
第十五周：
7.1 对称矩阵的对角化
7.2 二次型
Week 16:
Review
第十六周：
学期复习
18.
教材及其它参考资料 Textbook and Supplementary Readings
教材 Textbook: David C. Lay, Steven R. Lay, Judi J. McDonald, Linear Algebra and its Applications, Fifth Edition,
Pearson 2016, ISBN 13: 978-1-292-09223-2.
参考书/Supplementary Readings:
线性代数，第六版，同济大学数学系编，2014，ISBN: 978-7-04-039661-4.
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
7
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
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