东北大学：某学院应用统计学专业《线性代数》课程教学大纲

线性代数教学大纲Linear AlgebraSubject Syllabus，课程信息SubjectInformation课程编号：开课学期：2EQV-AS-37233Subject IDSemester课程分类：所属课群：专业教育PA专业基础MFCategorySection课程学分：总学时/周：348/12Credit PointsTotal Hours/Weeks理论学时：实验学时：480LECT. HoursEXP. HoursPBL学时:实践学时/周：00PBL HoursPRAC.Hours/Weeks开课学院：东北大学适用专业：应用统计学 ASCollege悉尼智能科技学院Stream课程属性：课程模式：必修Compulsory互认EQVPatternMode刘建波中方课程协调人成绩记载方式：百分制MarksNEU CoordinatorLiu JianboResult Type先修课程：无NoneRequisites1. Steven J.Leon, Linear Algebra with Applications, Ninth Edition,Chine Machine Press, 2020.英文参考教材2. Ron Larson, Elementary Linear Algebra, Cengage Learning, 2017.ENTextbooks3. Sun Xiaojuan, Linear Algebra, Beijing University of Posts andTelecommunicationsPress,20181.史蒂文J.利昂著，张文博，张丽静译，线性代数，机械工业出版社，2020中文参考教材：2.北京大学数学系，高等代数（第四版)，高等教育出版社，2013.CN Textbooks3.刘建波，大学教材全解-高等代数，延边大学出版社，20134.同济大学数学系.线性代数（第五版），高等教育出版社，2007教学资源：https://sstc.cloudcampus.com.cn/course/view.php?id-9Resources刘建波课程负责人(撰写人)：提交日期：3/8/2023Liu JianboSubmitted DateSubject Director刘建波任课教师(含负责人)：Taught byLiu Jianbo审核人：批准人：韩鹏史闻博Checked byApproved by批准日期：3/10/2023Approved Date1/10

1 / 10 线性代数 教学大纲 Linear Algebra Subject Syllabus 一、课程信息 Subject Information 课程编号: Subject ID EQV-AS-37233 开课学期: Semester 2 课程分类: Category 专业教育 PA 所属课群: Section 专业基础 MF 课程学分: Credit Points 3 总学时/周: Total Hours/Weeks 48/12 理论学时: LECT. Hours 48 实验学时: EXP. Hours 0 PBL 学时: PBL Hours 0 实践学时/周: PRAC. Hours/Weeks 0 开课学院: College 东北大学 悉尼智能科技学院 适用专业: Stream 应用统计学 AS 课程属性: Pattern 必修 Compulsory 课程模式: Mode 互认 EQV 中方课程协调人: NEU Coordinator 刘建波 Liu Jianbo 成绩记载方式: Result Type 百分制 Marks 先修课程: Requisites 无 None 英文参考教材: EN Textbooks 1. Steven J. Leon, Linear Algebra with Applications, Ninth Edition, Chine Machine Press, 2020. 2. Ron Larson, Elementary Linear Algebra, Cengage Learning, 2017. 3. Sun Xiaojuan, Linear Algebra, Beijing University of Posts and Telecommunications Press, 2018. 中文参考教材: CN Textbooks 1. 史蒂文 J. 利昂 著，张文博，张丽静 译，线性代数，机械工业 出版社, 2020. 2. 北京大学数学系，高等代数(第四版), 高等教育出版社, 2013. 3. 刘建波，大学教材全解-高等代数，延边大学出版社, 2013. 4. 同济大学数学系,线性代数(第五版), 高等教育出版社, 2007. 教学资源: Resources https://sstc.cloudcampus.com.cn/course/view.php?id=9 课程负责人(撰写人): Subject Director 刘建波 Liu Jianbo 提交日期: Submitted Date 3/8/2023 任课教师(含负责人): Taught by 刘建波 Liu Jianbo 审核人: Checked by 韩鹏 批准人: Approved by 史闻博 批准日期: Approved Date 3/10/2023

二、教学目标SubjectLearningObjectives(SLOs)注：毕业要求及指标点可参照悉尼学院本科生培养方案，可根据实际情况增减行数Note: GA and index can be referred from undergraduate program in SSTC website. Please add/reduce lines based on subject线性代数作为一种基本的数学工具在数学领域及其他科学领域，如控制理论、数值分析、信息与科学技术、最优化理论、管理科学等学科都有十分重要的应用。通过这门课程，学生可以了解矩阵分析在人类生活和社会发展中的重要地位和作用以及其深远的发展历史。同时学生能够系统掌握代数中的基本概念、基本理论和基本论证方法，提高学生从事科学研究的能力，为进一步学习其它专业课和从事专业研究打下基础。在奠定数学科学知识基础的同时，培养学生的基本运算能力、抽象思维能力、逻辑推理能力和运用所学的知识分析问题、解决问题的能力。培养科学精神、创新意识与应用意识。能够在多学科背景下的团队中承担个体、团队成员以及负责人的角色。Linear algebra, as a basic mathematical tool, has been applied veryimportantin mathematics andotherscientificfields,suchas controltheory,numerical analysis, information and science and technology整体目标：optimization theory,management science and other disciplinesOverallObjectiveThrough this course, students can understand the important position androleofmatrixanalysisinhuman lifeand socialdevelopmentaswell asits far-reaching development history.At the same time, students cansystematically master the basic concepts, basic theories and basicdemonstration methods of algebra, improve the ability of students toengage in scientific research, and lay a foundation for further learningother specialized courses and engaging in professional research. At thesametimeof laying thefoundation ofmathematical scienceknowledgethe students'basic operation ability,abstract thinking ability,logicalreasoning ability and the ability to use the learned knowledge toanalyzeand solveproblemswill be cultivated.Cultivate scientific spirit, innovation consciousness and applicationconsciousness.Abilityto work as an individual, a team member and aleaderinamultidisciplinaryteam具有扎实的专业基础与学科特长，系统掌握统计与数据分析、智能仿真建模技术、量化管理优化技术、试验设计与分析、项目管理与决策及其相关领域的专门知识与技能。A solid professional foundation and competency, systematical1-1mastery of the specialized knowledge and skills in statistics anddata analysis, intelligent simulation modeling technology,（1）专业目标：quantitativemanagementoptimizationtechnology,Professional Abilityexperimental design and analysis, project management anddecision-making具有扎实的专业基础与学科特长，系统掌握信息通信系统、项目管理与决策及其相关领域专门知识与技能。1-2Have a solid professional foundation and subject expertisemastertheinformationand communicationsystem,project2 /10

2 / 10 二、教学目标 Subject Learning Objectives (SLOs) 注：毕业要求及指标点可参照悉尼学院本科生培养方案，可根据实际情况增减行数 Note: GA and index can be referred from undergraduate program in SSTC website. Please add/reduce lines based on subject. 整体目标: Overall Objective 线性代数作为一种基本的数学工具在数学领域及其他科学领域，如 控制理论、数值分析、信息与科学技术、最优化理论、管理科学等 学科都有十分重要的应用。通过这门课程，学生可以了解矩阵分析 在人类生活和社会发展中的重要地位和作用以及其深远的发展历 史。同时学生能够系统掌握代数中的基本概念、基本理论和基本论 证方法，提高学生从事科学研究的能力，为进一步学习其它专业课 和从事专业研究打下基础。在奠定数学科学知识基础的同时，培养 学生的基本运算能力、抽象思维能力、逻辑推理能力和运用所学的 知识分析问题、解决问题的能力。培养科学精神、创新意识与应用 意识。能够在多学科背景下的团队中承担个体、团队成员以及负责 人的角色。 Linear algebra, as a basic mathematical tool, has been applied very important in mathematics and other scientific fields, such as control theory, numerical analysis, information and science and technology, optimization theory, management science and other disciplines. Through this course, students can understand the important position and role of matrix analysis in human life and social development as well as its far-reaching development history. At the same time, students can systematically master the basic concepts, basic theories and basic demonstration methods of algebra, improve the ability of students to engage in scientific research, and lay a foundation for further learning other specialized courses and engaging in professional research. At the same time of laying the foundation of mathematical science knowledge, the students' basic operation ability, abstract thinking ability, logical reasoning ability and the ability to use the learned knowledge to analyze and solve problems will be cultivated. Cultivate scientific spirit, innovation consciousness and application consciousness. Ability to work as an individual, a team member and a leader in a multidisciplinary team. （1）专业目标: Professional Ability 1-1 具有扎实的专业基础与学科特长，系统掌握统计与数据分 析、智能仿真建模技术、量化管理优化技术、试验设计与分 析、项目管理与决策及其相关领域的专门知识与技能。 A solid professional foundation and competency, systematical mastery of the specialized knowledge and skills in statistics and data analysis, intelligent simulation modeling technology, quantitative management optimization technology, experimental design and analysis, project management and decision-making. 1-2 具有扎实的专业基础与学科特长，系统掌握信息通信系统、 项目管理与决策及其相关领域专门知识与技能。 Have a solid professional foundation and subject expertise, master the information and communication system, project

management and decision-making and related fields ofexpertise and skills具有扎实的专业基础与学科特长，系统掌握大数据与人工智能系统、项目管理与决策及其相关领域专门知识与技能。Have a solid professional foundation and subject expertise1-3systematically master big data and artificial intelligencesystems, project management and decision-making and relatedfields of expertise and skills具有卓越的技术素养和突出的应用统计学实践能力，具备在应用统计学及其相关领域通过科学技术理论和方法创造性的解决复杂问题、从事学术前沿问题研究的能力。Have excellent technical literacy and outstanding practical1-4ability of applied statistics,have theability to creativelysolvecomplexproblemsthroughscientificandtechnologicaltheoriesand methods in Applied Statisticsand related fields,andengage in the research of academic frontier problems融入辩证唯物主义哲学思想，提升学生对概念、定理的认识深度和对本质的把握，促进学生辩证思维能力的培养。Integrate dialectical materialism philosophy thought, improve2-1students'understandingdepth of concept, theorem and grasp ofessence,and promote the cultivation of studentsdialecticalthinking ability线性代数的理论不仅渗透到了数学的许多分支中，而且在理论物理、理论化学、工程技术、国民经济、生物技术、航天、航海等领域中都有着广泛的应用。该课程对于培养学生的逻（2）德育目标：辑推理和抽象思维能力、空间直观和想象能力具有重要的作Essential Quality用。The theory of linear algebra has not only penetrated into many2-2branches of mathematics,but alsohas a wide range ofapplications in theoretical physics, theoretical chemistry,engineering technology,national economy,biotechnology,aerospace, navigation and other fields. This course plays animportant role in cultivating students' logical reasoning andabstract thinking ability, spatial intuition and imaginationability课程教学目标与毕业要求的对应关系MatrixofGA&SLOs毕业要求GA指标点GAIndex教学目标SLOs1、理学知识：具有扎实的数指标点1-1：具有较强的演绎推理能力、学基础，能够将数学、自然准确计算能力、分析归纳能力、抽象思科学和专业知识用于解决复维能力，掌握数学、自然科学和相关专杂实际问题。业知识，并使用其建立正确的数学、物1-1. 1-2Science knowledge: have a理学等模型以解释复杂实际问题。solid mathematicalHave strong deductive reasoning ability,foundation, be able to useaccurate calculation ability,analytical and3/10

3 / 10 management and decision-making and related fields of expertise and skills. 1-3 具有扎实的专业基础与学科特长，系统掌握大数据与人工智 能系统、项目管理与决策及其相关领域专门知识与技能。 Have a solid professional foundation and subject expertise, systematically master big data and artificial intelligence systems, project management and decision-making and related fields of expertise and skills. 1-4 具有卓越的技术素养和突出的应用统计学实践能力，具备在 应用统计学及其相关领域通过科学技术理论和方法创造性 的解决复杂问题、从事学术前沿问题研究的能力。 Have excellent technical literacy and outstanding practical ability of applied statistics, have the ability to creatively solve complex problems through scientific and technological theories and methods in Applied Statistics and related fields, and engage in the research of academic frontier problems. （2）德育目标: Essential Quality 2-1 融入辩证唯物主义哲学思想，提升学生对概念、定理的认识 深度和对本质的把握，促进学生辩证思维能力的培养。 Integrate dialectical materialism philosophy thought, improve students' understanding depth of concept, theorem and grasp of essence, and promote the cultivation of students' dialectical thinking ability. 2-2 线性代数的理论不仅渗透到了数学的许多分支中，而且在理 论物理、理论化学、工程技术、国民经济、生物技术、航天、 航海等领域中都有着广泛的应用。该课程对于培养学生的逻 辑推理和抽象思维能力、空间直观和想象能力具有重要的作 用。 The theory of linear algebra has not only penetrated into many branches of mathematics, but also has a wide range of applications in theoretical physics, theoretical chemistry, engineering technology, national economy, biotechnology, aerospace, navigation and other fields. This course plays an important role in cultivating students' logical reasoning and abstract thinking ability, spatial intuition and imagination ability. 课程教学目标与毕业要求的对应关系 Matrix of GA & SLOs 毕业要求 GA 指标点 GA Index 教学目标 SLOs 1、理学知识：具有扎实的数 学基础，能够将数学、自然 科学和专业知识用于解决复 杂实际问题。 Science knowledge: have a solid mathematical foundation, be able to use 指标点 1-1：具有较强的演绎推理能力、 准确计算能力、分析归纳能力、抽象思 维能力，掌握数学、自然科学和相关专 业知识，并使用其建立正确的数学、物 理学等模型以解释复杂实际问题。 Have strong deductive reasoning ability, accurate calculation ability, analytical and 1-1, 1-2

mathematics, natural scienceinductive ability, abstract thinking ability,andprofessional knowledgetomastermathematics,natural scienceandrelated professional knowledge, and use itsolve complexpracticalproblems.toestablishcorrectmathematicalphysicaland other models toexplain complexpracticalproblems.2-1能运用应用统计学的基本原理分析、识别和阐述与本专业相关的复杂实际问1、问题分析：能够借助应题。1-2, 1-3, 2-1用统计学的基本原理、方法Capable of analyzing, identifying and和手段，识别、表达、并通elaboratingcomplexpracticalproblems过文献研究分析复杂实际问related to this major with the applying of题，以获得有效结论。thebasicprinciples ofApplied Statistics2-2能够应用数学、自然科学和工程学的Problem analysis: with the基本原理、方法和手段，针对实际复杂help of the basic principles.工程问题设计针对性的技术方案，并综methodsandmeansofapplied合运用文献、科学基座和技术手段予以statistics, we can identify,解决。express and analyze complex1-3, 1-4, 2-1, 2-2Capable of drawing on the basic principlespractical problems throughliterature research,so astoof applied statistics to design targetedobtaineffectiveconclusionsschemesfor complexpracticalproblems,and using literature, scientific theories andtechnical means to solve them.三、教学内容 Content(Topics)注：以中英文填写，各部分内容的表格可根据实际知识单元数量进行复制、扩展或缩减Note: Filled in both CN and EN, extend or reduce based on the actual numbers ofknowledge unit(1)理论教学Lecture知识单元序号支撑教学目标11-1, 1-2, 1-3, 1-4Knowledge Unit NoSLOs Supported知识单元名称矩阵乘法和行列式Unit TitleMatrixmultiplication and determinants矩阵的定义Definition of matrix矩阵的初等变换，行最简型矩阵，矩阵的运算Fundamental transformation of matrix,Thesimplestrow form of知识点：matrix,ComputationofmatrixKnowledge Delivery分块矩阵，矩阵运算性质，矩阵的逆Blockmatrix,propertiesofmatrixcomputation,Inverseofmatrix初等矩阵；行列式定义，行列式的运算Fundamental matrix, Definition of determinant, Computation ofdeterminant4/10

4 / 10 mathematics, natural science and professional knowledge to solve complex practical problems. inductive ability, abstract thinking ability, master mathematics, natural science and related professional knowledge, and use it to establish correct mathematical, physical and other models to explain complex practical problems. 1、问题分析: 能够借助应 用统计学的基本原理、方法 和手段，识别、表达、并通 过文献研究分析复杂实际问 题，以获得有效结论。 Problem analysis: with the help of the basic principles, methods and means of applied statistics, we can identify, express and analyze complex practical problems through literature research, so as to obtain effective conclusions. 2-1 能运用应用统计学的基本原理分析、 识别和阐述与本专业相关的复杂实际问 题。 Capable of analyzing, identifying and elaborating complex practical problems related to this major with the applying of the basic principles of Applied Statistics. 1-2, 1-3, 2-1 2-2 能够应用数学、自然科学和工程学的 基本原理、方法和手段，针对实际复杂 工程问题设计针对性的技术方案，并综 合运用文献、科学基座和技术手段予以 解决。 Capable of drawing on the basic principles of applied statistics to design targeted schemes for complex practical problems, and using literature, scientific theories and technical means to solve them. 1-3, 1-4, 2-1, 2-2 三、教学内容 Content (Topics) 注：以中英文填写，各部分内容的表格可根据实际知识单元数量进行复制、扩展或缩减 Note: Filled in both CN and EN, extend or reduce based on the actual numbers of knowledge unit (1) 理论教学 Lecture 知识单元序号: Knowledge Unit No. 1 支撑教学目标: SLOs Supported 1-1，1-2，1-3，1-4 知识单元名称 Unit Title 矩阵乘法和行列式 Matrix multiplication and determinants 知识点: Knowledge Delivery 矩阵的定义 Definition of matrix 矩阵的初等变换，行最简型矩阵, 矩阵的运算 Fundamental transformation of matrix, The simplest row form of matrix, Computation of matrix 分块矩阵，矩阵运算性质，矩阵的逆 Block matrix, properties of matrix computation, Inverse of matrix 初等矩阵；行列式定义，行列式的运算 Fundamental matrix, Definition of determinant, Computation of determinant

行列式定义，分块矩阵定义，线性方程组定义了解：Definition of determinant, block matrix, linear equationRecognizesystem初等变换方法，矩阵的逆求法理解：学习目标：Fundamental transformation methodLearning ObjectivesUnderstandMethod of inverse of matrix矩阵运算性质，行列式的运算掌握：Properties of matrix computation,Computation ofMasterdeterminant2-1理解高等数学理论知识对于刻画工程实践问题的重要意义。德育目标Understand the significant meanings of theadvanced mathematics inMoral Objectivesdepictingthepracticalengineeringproblems初等变换方法，矩阵的逆求法重点：Fundamental transformation method.Key PointsMethod of inverse of matrix难点：矩阵运算性质，行列式的运算Focal pointsPropertiesofmatrixcomputation,Computationofdeterminant知识单元序号支撑教学目标：21-1, 1-2Knowledge Unit No.SLOs Supported知识单元名称线性方程组和向量空间Unit TitleSystems of linear equations and Vector spaces向量，向量空间，向量子空间Vectors,Vectorspaces,Subspacesofvectorspaces生成集和线性无关，基和维数Spanning sets and linearindependence,Basis anddimension;知识点：矩阵的秩和线性方程组Rankofamatrixand systemsof linearKnowledge Deliveryequations;坐标和基变换Coordinatesandchangeofbasis内积空间，正交基,施密特正交化过程Innerproductspaces,Orthonormal bases, Gram-schmidt process向量，向量空间，向量子空间,Vectors，Vector了解：spaces,Subspacesofvector spacesRecognize生成集，基和维数Spanningsets,Basisanddimension坐标和基变换；Coordinatesandchangeofbasis；理解：内积，正交和正交集Innerproducts,OrthogonalandUnderstand学习目标：orthonormal sets;Learning Objectives线性相关和线性无关，Lineardependenceand linearindependence;掌握：矩阵的秩和线性方程组RankofamatrixandsystemsMasterof linearequations:施密特正交化过程Gram-schmidtprocess德育目标2-2认知当前全球，数学理论的发展对提升中国工程关键技术及核Moral Objectives心竞争力的重要意义。5/10

5 / 10 学习目标: Learning Objectives 了解: Recognize 行列式定义, 分块矩阵定义，线性方程组定义 Definition of determinant, block matrix, linear equation system 理解: Understand 初等变换方法，矩阵的逆求法 Fundamental transformation method, Method of inverse of matrix 掌握: Master 矩阵运算性质，行列式的运算 Properties of matrix computation, Computation of determinant 德育目标 Moral Objectives 2-1 理解高等数学理论知识对于刻画工程实践问题的重要意义。 Understand the significant meanings of the advanced mathematics in depicting the practical engineering problems. 重点: Key Points 初等变换方法，矩阵的逆求法 Fundamental transformation method, Method of inverse of matrix 难点: Focal points 矩阵运算性质，行列式的运算 Properties of matrix computation, Computation of determinant 知识单元序号: Knowledge Unit No. 2 支撑教学目标: SLOs Supported 1-1，1-2 知识单元名称 Unit Title 线性方程组和向量空间 Systems of linear equations and Vector spaces 知识点: Knowledge Delivery 向量,向量空间,向量子空间 Vectors,Vector spaces, Subspaces of vector spaces 生成集和线性无关, 基和维数 Spanning sets and linear independence，Basis and dimension； 矩阵的秩和线性方程组 Rank of a matrix and systems of linear equations； 坐标和基变换 Coordinates and change of basis 内积空间，正交基,施密特正交化过程 Inner product spaces,Orthonormal bases, Gram-schmidt process 学习目标: Learning Objectives 了解: Recognize 向量,向量空间,向量子空间,Vectors, Vector spaces,Subspaces of vector spaces 生成集,基和维数 Spanning sets, Basis and dimension; 理解: Understand 坐标和基变换；Coordinates and change of basis； 内积, 正交和正交集 Inner products, Orthogonal and orthonormal sets； 掌握: Master 线性相关和线性无关,Linear dependence and linear independence; 矩阵的秩和线性方程组 Rank of a matrix and systems of linear equations； 施密特正交化过程 Gram-schmidt process 德育目标 Moral Objectives 2-2 认知当前全球，数学理论的发展对提升中国工程关键技术及核 心竞争力的重要意义

Understand the technology development, key techniques and the corecompetitiveness in the area of the China engineering in the world2-3培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难而上的精神，并在学习过程中培养自己的细心和耐心的勇气和精神Cultivatethe spirit of notfearing difficulties or failure,perseverancedaring to try,and cultivate their own careful and patient courage andspirit in the process of learning2-4培养服务意识，具有“以人为本”的服务精神Cultivate serviceconsciousness and have theservice spirit of"people-oriented"线性相关和线性无关Lineardependenceand linearindependence;重点：矩阵的秩和线性方程组Rankofamatrixand systems oflinearKey Pointsequations:难点施密特正交化过程Gram-schmidtprocessFocal points知识单元序号支撑教学目标31-1, 1-2, 2-1, 2-2Knowledge Unit No.SLOs Supported线性变换知识单元名称Unit TitleLinear transformation线性变换的定义Thedefinitionofalineartransformation线性变换的矩阵表示知识点：Amatrix representation of a linear transformationKnowledge Delivery线性变换的矩阵相似Thematrix similarity of lineartransformations线性变换的值域与核Range and kernel of linear transformation了解：线性变换的定义The definition ofa linear transformationRecognize线性变换的标准矩阵表示，值域与核理解：学习目标StandardoflinearmatrixrepresentationUnderstandLearning Objectivestransformations, range and kernel矩阵表示定理及应用以及相似性掌握：Matrix representation theorem and its application andMastersimilarity培养学生用哲学思辨立场、观点和方法分析解决问题，能够提高学生的创新能力和应用意识。德育目标Cultivating students to analyze and solve problems with philosophicalMoral Objectivesthinking standpoint, viewpoint and method can improve studentsinnovation ability and application consciousness.重点：矩阵表示定理及其应用Key PointsMatrixrepresentation theoremand itsapplication同一线性变换在不同基下的矩阵表示是相似的难点：The matrix representation of the same linear transformation onFocal pointsdifferent bases is similar6/10

6 / 10 Understand the technology development, key techniques and the core competitiveness in the area of the China engineering in the world. 2-3 培养具有不畏困难、不惧失败、锲而不舍、敢于尝试、迎难而 上的精神，并在学习过程中培养自己的细心和耐心的勇气和精神 Cultivate the spirit of not fearing difficulties or failure, perseverance, daring to try, and cultivate their own careful and patient courage and spirit in the process of learning 2-4 培养服务意识，具有“以人为本” 的服务精神 Cultivate service consciousness and have the service spirit of "people-oriented" 重点: Key Points 线性相关和线性无关 Linear dependence and linear independence; 矩阵的秩和线性方程组 Rank of a matrix and systems of linear equations； 难点: Focal points 施密特正交化过程 Gram-schmidt process 知识单元序号: Knowledge Unit No. 3 支撑教学目标: SLOs Supported 1-1，1-2，2-1，2-2 知识单元名称 Unit Title 线性变换 Linear transformation 知识点: Knowledge Delivery 线性变换的定义 The definition of a linear transformation 线性变换的矩阵表示 A matrix representation of a linear transformation 线性变换的矩阵相似 The matrix similarity of linear transformations 线性变换的值域与核 Range and kernel of linear transformation 学习目标: Learning Objectives 了解: Recognize 线性变换的定义 The definition of a linear transformation 理解: Understand 线性变换的标准矩阵表示，值域与核 Standard matrix representation of linear transformations, range and kernel 掌握: Master 矩阵表示定理及应用以及相似性 Matrix representation theorem and its application and similarity 德育目标 Moral Objectives 培养学生用哲学思辨立场、观点和方法分析解决问题，能够提高学 生的创新能力和应用意识。 Cultivating students to analyze and solve problems with philosophical thinking standpoint, viewpoint and method can improve students' innovation ability and application consciousness. 重点: Key Points 矩阵表示定理及其应用 Matrix representation theorem and its application 难点: Focal points 同一线性变换在不同基下的矩阵表示是相似的 The matrix representation of the same linear transformation on different bases is similar

知识单元序号支撑教学目标：X1-4,2-1,2-2Knowledge Unit No.SLOs Supported知识单元名称特征值与特征向量Unit TitleEigenvalues andEigenvectors特征值与特征向量的定义Definitions of eigenvalues and eigenvectors对角化知识点：DiagonalizationKnowledge Delivery矩阵可对角化的条件Conditionsfordiagonalizationof matrices相似矩阵和正交对角化Symmetric matrices and orthogonal diagonalization了解：特征值与特征向量的定义RecognizeDefinitions of eigenvalues and eigenvectors理解：对角化学习目标：UnderstandDiagonalizationLearning Objectives矩阵可对角化的条件掌握：The condition ofmatrixdiagonalizationMaster相似矩阵和正交对角化Symmetric matrices and orthogonal diagonalization在计算机日益普及的今天，解大型线性方程组、求矩阵的特征值、特征向量等已经成为工程技术人员经常遇到的课题，因此本课程所介绍的方法广泛地应用于各个学科，这就要求工科学生必须具备有线性代数基本理论知识，并熟练地掌握它的方法。为今后学习代数学和其它学科及进一步提高打下必要的数学基础。Today,the increasing popularity of computer, large linear equations,德育目标matrix eigenvalue and eigenvector and so on has become a subject ofMoral Objectivesengineering and technical personnel often encountered, so this courseintroduced methods widely used in various disciplines, this requiresengineering students must have the basic theory of linear algebraknowledge,and skillfullymasterthemethods of it.Forthefuture studyof algebra and other subjects and further improve to lay the necessarymathematicalfoundation重点：矩阵可对角化的条件Key PointsThe condition of matrix diagonalization难点：相似矩阵和正交对角化Focal pointsSymmetricmatrices andorthogonal diagonalization知识单元序号支撑教学目标：51-4, 2-1, 2-2Knowledge Unit No.SLOs Supported二次型知识单元名称Unit TitleQuadraticForms实二次型和其矩阵Realquadraticformand itsmatrix知识点实二次型的标准型CanonicalformofrealquadraticformKnowledge Delivery正定二次型和正定矩阵Positivedefinitequadraticformandmatrices7/10

7 / 10 知识单元序号: Knowledge Unit No. 4 支撑教学目标: SLOs Supported 1-4，2-1，2-2 知识单元名称 Unit Title 特征值与特征向量 Eigenvalues and Eigenvectors 知识点: Knowledge Delivery 特征值与特征向量的定义 Definitions of eigenvalues and eigenvectors 对角化 Diagonalization 矩阵可对角化的条件 Conditions for diagonalization of matrices 相似矩阵和正交对角化 Symmetric matrices and orthogonal diagonalization 学习目标: Learning Objectives 了解: Recognize 特征值与特征向量的定义 Definitions of eigenvalues and eigenvectors 理解: Understand 对角化 Diagonalization 掌握: Master 矩阵可对角化的条件 The condition of matrix diagonalization 相似矩阵和正交对角化 Symmetric matrices and orthogonal diagonalization 德育目标 Moral Objectives 在计算机日益普及的今天，解大型线性方程组、求矩阵的特征值、 特征向量等已经成为工程技术人员经常遇到的课题，因此本课程所 介绍的方法广泛地应用于各个学科，这就要求工科学生必须具备有 线性代数基本理论知识，并熟练地掌握它的方法。为今后学习代数 学和其它学科及进一步提高打下必要的数学基础。 Today, the increasing popularity of computer, large linear equations, matrix eigenvalue and eigenvector and so on has become a subject of engineering and technical personnel often encountered, so this course introduced methods widely used in various disciplines, this requires engineering students must have the basic theory of linear algebra knowledge, and skillfully master the methods of it. For the future study of algebra and other subjects and further improve to lay the necessary mathematical foundation. 重点: Key Points 矩阵可对角化的条件 The condition of matrix diagonalization 难点: Focal points 相似矩阵和正交对角化 Symmetric matrices and orthogonal diagonalization 知识单元序号: Knowledge Unit No. 5 支撑教学目标: SLOs Supported 1-4，2-1，2-2 知识单元名称 Unit Title 二次型 Quadratic Forms 知识点: Knowledge Delivery 实二次型和其矩阵 Real quadratic form and its matrix 实二次型的标准型 Canonical form of real quadratic form 正定二次型和正定矩阵 Positive definite quadratic form and matrices

二次型的应用Theapplicationofthequadraticform了解：实二次型和其矩阵RealquadraticformanditsmatrixRecognize实二次型的标准型Canonicalformofrealquadratic理解：form学习目标：Understand正定二次型和正定矩阵PositivedefinitequadraticLearning Objectivesform and matrices二次型的应用Theapplicationofthequadraticform掌握：正定二次型和正定矩阵PositivedefinitequadraticMasterform and matrices掌握数学的基本思维和科学方法，树立科学思想，崇尚科学精神。德育目标Master the basic thinking and scientific method of mathematicsMoral Objectivesestablishscientificthoughtand advocatescientificspirit重点：二次型的应用TheapplicationofthequadraticformKey Points正定矩阵Positivedefinitequadraticformandmatrices难点：正定矩阵PositivedefinitequadraticformandmatricesFocal points四、教学安排Teaching Schedule注：可根据实际情况增减行数Note: Please add/reduce lines based on subject.学时(周）Hour(Week)教学内容TeachingContent理论实验课外实践集中实践LECT.EXP.PBLPRAC.矩阵和行列式10000Matrices anddeterminants线性方程组和向量空间00120Systemsof linearequationsandVectors space线性变换01200Transformations特征值和特征向量8000Eigenvalues and Eigenvectors二次型6000QuadraticForms总计 Total48000五、教学方法TeachingMethodology注：可根据实际情况增减行数或修改内容Note: Please add/reduce lines or revise content based on subject8/10

8 / 10 二次型的应用 The application of the quadratic form 学习目标: Learning Objectives 了解: Recognize 实二次型和其矩阵 Real quadratic form and its matrix 理解: Understand 实二次型的标准型 Canonical form of real quadratic form 正定二次型和正定矩阵 Positive definite quadratic form and matrices 掌握: Master 二次型的应用 The application of the quadratic form 正定二次型和正定矩阵 Positive definite quadratic form and matrices 德育目标 Moral Objectives 掌握数学的基本思维和科学方法，树立科学思想，崇尚科学精神。 Master the basic thinking and scientific method of mathematics, establish scientific thought and advocate scientific spirit. 重点: Key Points 二次型的应用 The application of the quadratic form 正定矩阵 Positive definite quadratic form and matrices 难点: Focal points 正定矩阵 Positive definite quadratic form and matrices 四、教学安排 Teaching Schedule 注：可根据实际情况增减行数 Note: Please add/reduce lines based on subject. 教学内容 Teaching Content 学时(周) Hour(Week) 理论 LECT. 实验 EXP. 课外实践 PBL 集中实践 PRAC. 矩阵和行列式 Matrices and determinants 10 0 0 0 线性方程组和向量空间 Systems of linear equations and Vectors space 12 0 0 0 线性变换 Transformations 12 0 0 0 特征值和特征向量 Eigenvalues and Eigenvectors 8 0 0 0 二次型 Quadratic Forms 6 0 0 0 总计 Total 48 0 0 0 五、教学方法 Teaching Methodology 注：可根据实际情况增减行数或修改内容 Note: Please add/reduce lines or revise content based on subject

勾选Check教学方法与特色TeachingMethodology&Characters多媒体教学：基于信息化设备的课堂教学团Multi-media-based lecturing实践能力传授：理论与行业、实际案例相结合团Combining theory with industrial practical problems课程思政建设：知识讲授与德育相结合Knowledgedelivery with ethic educationPBL教学：问题驱动的分组学习与交流团Problem-based learning其他：单击或点击此处输入文字。口Other:单击或点击此处输入文字。六、成绩评定Assessment注：可根据实际情况增减行数或修改内容Note: Please add/reduce lines or revise content based on subject.考核环节：刘建波环节负责人：平时BehaviorAssessment ContentDirectorLiu Jianbo给分形式课程总成绩比重(%):30百分制MarksResult TypePercentage (%)平时成绩，以学生平时课堂表现、课堂教师随机提问，学生平时作业完成情况综合评定，其中，学生平时课堂表现、课堂教师随机提问占比10%，学生平时作业（课前预习作业、课后作业完成情况占考核方式：比90%.MeasuresAccording to instant answer to the teacher's questions, comprehensivereportandquestion performance,themark isevaluated,where questionperformance and instant answer accounts for 10%,assignmentsperformance (pre-lecture and post-lecture)accounts for90%考核环节：环节负责人：刘建波期中Mid-termAssessment ContentDirectorLiu Jianbo给分形式：课程总成绩比重(%)：20百分制MarksResult TypePercentage (%)120分钟Thresholdtest，共计2次，每次考试满分100分，每次考试成绩占Thresholdtest的比例，与课程知识点学时占总理论学时的比例，保持一致.该部分成绩列入期中考试成绩科目。考核方式One hundred and twenty minutes Threshold text, there are totally twoMeasurestests, thefull mark is 100 mark and percentage of each test accountingon the final mark conforms to the samepercentage of correspondingtheoretical term hour accounting on the wholetheoretical term hour.Themarks are listed in themid-term exam score.9/10

9 / 10 勾选 Check 教学方法与特色 Teaching Methodology & Characters  多媒体教学：基于信息化设备的课堂教学 Multi-media-based lecturing  实践能力传授：理论与行业、实际案例相结合 Combining theory with industrial practical problems  课程思政建设：知识讲授与德育相结合 Knowledge delivery with ethic education  PBL 教学：问题驱动的分组学习与交流 Problem-based learning ☐ 其他:单击或点击此处输入文字。 Other:单击或点击此处输入文字。 六、成绩评定 Assessment 注：可根据实际情况增减行数或修改内容 Note: Please add/reduce lines or revise content based on subject. 考核环节: Assessment Content 平时 Behavior 环节负责人: Director 刘建波 Liu Jianbo 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 30 考核方式: Measures 平时成绩，以学生平时课堂表现、课堂教师随机提问，学生平时作 业完成情况综合评定，其中，学生平时课堂表现、课堂教师随机提 问占比 10%, 学生平时作业(课前预习作业、课后作业)完成情况占 比 90%. According to instant answer to the teacher's questions, comprehensive report and question performance, the mark is evaluated, where question performance and instant answer accounts for 10%, assignments performance (pre-lecture and post-lecture) accounts for 90%. 考核环节: Assessment Content 期中 Mid-term 环节负责人: Director 刘建波 Liu Jianbo 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 20 考核方式: Measures 120 分钟 Threshold test，共计 2 次，每次考试满分 100 分，每次考 试成绩占 Threshold test 的比例，与课程知识点学时占总理论学时的 比例，保持一致.该部分成绩列入期中考试成绩科目。 One hundred and twenty minutes Threshold text, there are totally two tests, the full mark is 100 mark and percentage of each test accounting on the final mark conforms to the same percentage of corresponding theoretical term hour accounting on the whole theoretical term hour. The marks are listed in the mid-term exam score

刘建波考核环节：环节负责人：期末FinalDirectorLiu JianboAssessment Content给分形式课程总成绩比重(%)50百分制MarksResult TypePercentage (%)满分100分，通过批阅期末考试试卷给出学生成绩。考核方式：A full score of 100 will be given by marking the final examinationMeasurespapers七，改进机制ImprovementMechanism注：未尽事宜以教学团队以及学院教学指导委员会商定为准。Note: Matters not covered in this file shall be determined by TAB of SSTC, NEU.教学大纲改进机制SubjectSyllabusImprovementMechanism考核周期(年):修订周期(年）44Check Period (YR)RevisePeriod (YR)课程负责人根据课程教学内容与人才培养目标组织课程团队讨论并修改教学大纲，报分管教学工作副院长审核后由执行院长批准。改进措施：Theperson inchargeof the course shall organizethe courseteamtoMeasuresdiscuss and revise the syllabus according to the courseteaching contentand talent training objectives, which shall be submitted to the vicepresident incharge of teachingfor approval by the executive president.成绩评定改进机制AssessmentImprovementMechanism考核周期(年)修订周期(年)11Check Period (YR)Revise Period (YR)课程负责人根据课程教学内容、课堂教学效果以及成绩分布，对课程教学方法和成绩评定环节进行改进，并同步优化评定办法。改进措施：Accordingtothecourseteachingcontent,classroomteaching effectMeasuresand score distribution,the person in charge of the course improves thecourse teaching method and score evaluation link,and optimizes theevaluation method at the same time.10/10

10 / 10 考核环节: Assessment Content 期末 Final 环节负责人: Director 刘建波 Liu Jianbo 给分形式: Result Type 百分制 Marks 课程总成绩比重(%): Percentage (%) 50 考核方式: Measures 满分 100 分，通过批阅期末考试试卷给出学生成绩。 A full score of 100 will be given by marking the final examination papers 七、改进机制 Improvement Mechanism 注：未尽事宜以教学团队以及学院教学指导委员会商定为准。 Note: Matters not covered in this file shall be determined by TAB of SSTC, NEU. 教学大纲改进机制 Subject Syllabus Improvement Mechanism 考核周期(年): Check Period (YR) 4 修订周期(年): Revise Period (YR) 4 改进措施: Measures 课程负责人根据课程教学内容与人才培养目标组织课程团队讨论 并修改教学大纲，报分管教学工作副院长审核后由执行院长批准。 The person in charge of the course shall organize the course team to discuss and revise the syllabus according to the course teaching content and talent training objectives, which shall be submitted to the vice president in charge of teaching for approval by the executive president. 成绩评定改进机制 Assessment Improvement Mechanism 考核周期(年): Check Period (YR) 1 修订周期(年): Revise Period (YR) 1 改进措施: Measures 课程负责人根据课程教学内容、课堂教学效果以及成绩分布，对课 程教学方法和成绩评定环节进行改进，并同步优化评定办法。 According to the course teaching content, classroom teaching effect and score distribution, the person in charge of the course improves the course teaching method and score evaluation link, and optimizes the evaluation method at the same time