syllabus of Linear algebra(最终版)

1SyllabusofLinearalgebraCode:Linearalgebra:130703X1Credits:2Credithours:32Prerequisites:ElementaryMathematicsSuitableFor：EngineeringStudents一、课程简介线性代数是大学理、工、农、经、管类的公共基础课，是我校各专业必备的基础数学课程，本课程的主要内容有：矩阵与线性方程组、行列式、几何空间、n维向量空间、特征值与特征向量、二次型。本课程是数学类课程：多元微积分、数学实验、数理方程、概率统计、矩阵理论、泛函分析、数学模型等课程的基础，也是物理类及理工、经管类专业课程的基础。Linearalgebraisapublicbasiccourseofengineering,medicine,agriculture,economyandmanagementsciencesinUniversity.Themaincontentsofthiscourseinclude:matrixandlinearequations,determinant,geometricalspace,vectorspace,eigenvalueandeigenvector,quadraticform.Thiscourseisthebasisforcalculus,mathematicalexperiment,mathematicalphysicalequation,probabilityandstatistics,matrixtheory,functionalanalysis,mathematicalmodeletc.,butalsothebasisforthephysicalandengineering,economicsandmanagementprofessionalcourses.二、课程目标课程的教学目标是使学生掌握本课程的主要知识，理解基本概念和基本理论，学会分析问题，解决问题的基本方法：了解各部分知识的结构及知识的内在联系；能运用基本概念；基本理论和基本方法正确地推理证明，准确、简捷地计算；能综合运用所学知识分析并解决简单的实际问题；培养学生的抽象思维能力、逻辑推理能力、空间想象能力、创造性思维能力和自学能力，为后续课程的学习奠定必要的数学基础。Theteachingaimofthiscourseistomakethestudentsmasterthemajorknowledgeofthecourse,tounderstandthebasicconceptsandbasictheory,basicmethodstoanalyzeand2solveproblems;tounderstandtheinternalconnectionstructureandknowledgeofeachpartofknowledge;cancorrectlyprovedtousethebasicconcepts,basictheoryandbasicmethods;canaccuratelyandquicklymakebasiccalculation;canusetheknowledgetosolvethesimplepracticalproblems.Tocultivatethestudents'abstractthinkingability,logicalreasoningability,spatialimaginationability,creativethinkingabilityandself-learningability,laythemathematicalfoundationsforfollowingcourses.三、课程内容安排和要求CourseContentsandRequirements第一章矩阵及初等变换(1)矩阵及其运算.(2)高斯消元法及矩阵的初等变换.(3)逆矩阵.(4)分块矩阵.ChapterOneMatrixandElementaryTransformation(1)Matrixanditsoperations.(2)Gaussianeliminationandmatrixelementarytransformation.(3)Inversematrix.(4)Blockmatrix.要求：1.矩阵、单位矩阵、数量矩阵、对角矩阵、三角矩阵、对称矩阵和反对称矩阵的概念与性质.2.矩阵的线性运算、乘法、转置，矩阵多项式的概念.3.矩阵的初等变换，用初等变换求逆矩的方法.Requirements:1.Conceptsandpropertiesofmatrix,unitmatrix,quantitymatrix,diagonalmatrix,triangularmatrix,symmetricmatrixandskewsymmetricmatrix.2.Matrixlinearoperation,multiplication,transpose,conceptofmatrixpolynomial.3.Elementarytransformationofthematrix,solveinversematrixbyelementarytransformation.第二章行列式(1)n阶行列式的定义、性质、运算.3(2)Laplace展开定理.(3)克拉默法则.(4)矩阵的秩.(1)Thedefinition,property,andoperationofthen-orderdeterminant.(2)Laplaceexpansiontheorem.(3)Cramer'srule.(4)rankofmatrix.要求：(1)用行列式的性质计算行列式.(2)方阵乘积，以及矩阵可逆的充分必要条件.(3)伴随矩阵的概念及使用（逆矩阵.(4)矩阵秩的概念、性质，用初等变换求矩阵秩.Requirements:(1)Calculatethedeterminantbythepropertiesofdeterminant.(2)Theproductofsquarematrix,andthesufficientandnecessaryconditionsforthematrixtobereversible.(3)Conceptanduseofadjugatematrix(inversematrix).(4)Theconceptandpropertyofmatrix,solvethematrixrankbyelementarytransformation.第三章几何空间(1)空间直角坐标系与向量.(2)向量的乘法.(3)平面.(4)空间直线.ChapterThreeGeometricSpace(1)SpaceCartesiancoordinatesystemandvector.(2)Vectormultiplication.(3)Plane.(4)Spacestraightline.4要求：(1)空间直角坐标系，向量的概念及其表示.(2)向量的运算（线性运算、数量积、向量积、混合积）.(3)向量的坐标表示及运算.(1)SpaceCartesiancoordinatesystem,theconceptofvectoranditsrepresentation.(2)Vectoroperation(linearoperation,quantityproduct,vectorproduct,mixedproduct).(3)Vectorcoordinaterepresentationandoperation.第四章n维向量空间(1)n维向量空间的概念.(2)向量组的线性相关性，秩，最大无关组.(3)线性方程组解的结构.ChapterFourn-dimensionalVectorSpace(1)Conceptofndimensionvectorspaceconcept.(2)Thelinearcorrelation,rank,andmaximumirrelevantgroupofvectorgroup.(3)TheStructureofsolutionsoflinearsystemofequations.要求：(1)向量的线性组合与线性表示.(2)向量组线性相关，线性无关的概念以及判别.(3)向量组的最大线性无关组和向量组的秩.(4)齐次线性方程组有非零解的充分必要条件及非齐次线性方程组有解的充分必要条件.(5)掌握齐次线性方程组的基础解系，通解及解空间的概念，求法.(6)非齐次线性方程组解的结构及通解的概念.(7)使用初等行变换求解线性方程组.Requirements:(1)Theconceptandjudgmentofvectorgrouplinearcorrelation,linearindependence.(2)Necessaryandsufficientconditionsfornonzerosolutionsofhomogeneouslinearsystemofequationsandnecessaryandsufficientconditionsforsolutionsofnon-homogeneouslinearsystemofequations.(3)Grasptheconceptandsolutionsofthebasicsolutionsystem,generalsolutionandsolutionspaceofnon-homogeneouslinearsystemofequations.(4)Theconceptofthestructureandgeneralsolutionofnon-homogeneouslinearsystemofequations5(5)Solvelinearsystemofequationsbyelementaryrowtransformation.第五章特征值与特征向量(1)特征值与特征向量的概念、计算.(2)矩阵的相似对角化.(3)n维向量空间的正交性.(4)实对称矩阵的相似对角化.ChapterFiveEigenvalueandEigenvector(1)Theconceptandcalculationofeigenvaluesandeigenvectors.(2)Similaritydiagonalizationofmatrices.(3)Orthogonalityofn-dimensionalvectorspaces.(4)SimilarityDiagonalizationofrealsymmetricmatrice.第六章二次型(1)实二次型及其标准形.(2)正定二次型.ChapterSixQuadratic(1)Realquadraticformanditsstandardshape(2)Positivedefinitequadratic