Withtherapiddevelopmentofbigdata,cloudcomputing,InternetofThings,artificialintelligenceandotherinformationtechnologies,modernsocietyisenteringthedataerainanall-roundway.Matrixalgebraisthebasiclanguageofthedataeraandhasbeenwidelyusedinvariousfieldsofmodernscienceandtechnology.Manypracticalproblemscanbediscretizedandlinearized,andthustransformedintolinearalgebraproblems.Forexample,thedesignofnetworksearchengines,aircraftdesign,bigdataprocessing,computerimageprocessing,3Danimation,virtualreality,etc.,everywherereflecttheperfectfusionofalgebra,geometryandtherealworld.
Thiscourseincludessixparts:determinant,matrix,linearcorrelationofvectorgroups,linearequationsystem,similartransformationofmatrix,quadraticform.
Chapter1Determinant
1.1Definitionofn-orderdeterminant
1.2Thepropertyofthedeterminant
1.3Expansionandcalculationofdeterminant
1.4Cramer\'srule
Chapter1DeterminantTest
Chapter2Matrix
2.1Theconceptofmatrix
2.2Matrixoperation
2.3Inversematrix
2.4blockmatrix
2.5Elementarytransformationandelementarymatrix
2.6Therankofthematrix
Chapter2MatrixTest
Chapter3Linearcorrelationofvectorgroups
3.1Theconceptandoperationofvector
3.2Linearcorrelationofvectorgroups
3.3Rankofvectorgroup
3.4VectorSpace
Chapter3LinearcorrelationofvectorgroupsTest
Chapter4Linearequations
4.0Theintroductionoftheproblem
4.1Thedecisiontheoremforthesolutionoflinearequations
4.2Thesolutionoflinearequations
4.3Structureofthesolutionoflinearequations
Chapter4LinearequationsTest
Chapter5Matrixsimilaritytransformation
5.1EigenvaluesandEigenvectorsofSquareMatrix
5.2Similardiagonalizationofmatrices
5.3Similardiagonalizationofrealsymmetricmatrices
Chapter5MatrixsimilaritytransformationTest
Chapter6Quadratic
6.1Quadraticformanditsmatrixrepresentation
6.2Turnquadraticformintostandardform
6.3Theinertiatheorem
6.4Positivedefinitequadraticformandpositivedefinitematrix