NumericalLinerAlgebrawithApplications

NumericalLinerAlgebrawithApplications
TOPICSChapters1-6providecoverageofappliedlinearalgebrasufficientforreadingtheremainderofthebook.Chapter1:MatricesThechapterintroducesmatrixarithmeticandtheveryimportanttopicoflineartransformations.Rotationmatricesprovideaninterestingandusefulexampleoflineartransformations.Afterdiscussingmatrixpowers,theconceptofthematrixinverseandtransposeconcludesthechapter.Chapter2:LinearEquationsThischapterintroducesGaussianeliminationforthesolutionoflinearsystemsAx=bandforthecomputationofthematrixinverse.Thechapteralsointroducestherelationshipbetweenthematrixinverseandthesolutiontoalinearhomogeneousequation.Twoapplicationsinvolvingatrussandanelectricalcircuitconcludethechapter.Chapter3:SubspacesThischapteris,byitsverynature,somewhatabstract.Itintroducestheconceptsofsubspaces,linearindependence,basis,matrixrank,range,andnullspace.Althoughthechaptermaychallengesomereaders,theconceptsareessentialforunderstandingmanytopicsinthebook,anditshouldbecoveredthoroughly.Chapter4:DeterminantsAlthoughthedeterminantisrarelycomputedinpractice,itisoftenusedinproofsofimportantresults.Thechapterintroducesthedeterminantanditscomputationusingexpansionbyminorsandbyrowelimination.Thechapterendswithaninterestingapplicationofthedeterminanttotextencryption.Chapter5:EigenvaluesandEigenvectorsThisisaveryimportantchapter,anditsresultsareusedthroughoutthebook.Afterdefiningtheeigenvalueandanassociatedeigenvector,thechapterdevelopssomeoftheirmostimportantproperties,includingtheiruseinmatrixdiagonalization.Thechapterconcludeswithanapplicationtothesolutionofsystemsofordinarydifferentialequationsandtheproblemofrankingitemsusingeigenvectors.Chapter6:OrthogonalVectorsandMatricesThischapterintroducestheinnerproductanditsassociati 本软件ID:8578431