applied linear algebra and matrix analysis - thomas s. shores

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1、APPLIEDLINEARALGEBRAANDMATRIXANALYSISThomasS.ShoresAuthoraddress:COPYRIGHTcMAY2000ALLRIGHTSRESERVEDContentsPrefaceiChapter1.LINEARSYSTEMSOFEQUATIONS11.1.SomeExamples11.2.NotationsandaReviewofNumbers91.3.GaussianElimination:BasicIdeas181.4.GaussianElimination:GeneralProcedure291.5.*

2、ComputationalNotesandProjects39Review47Chapter2.MATRIXALGEBRA492.1.MatrixAdditionandScalarMultiplication492.2.MatrixMultiplication552.3.ApplicationsofMatrixArithmetic622.4.SpecialMatricesandTransposes722.5.MatrixInverses852.6.BasicPropertiesofDeterminants962.7.*ApplicationsandProof

3、sforDeterminants1062.8.*TensorProducts1142.9.*ComputationalNotesandProjects118Review123Chapter3.VECTORSPACES1253.1.DefinitionsandBasicConcepts1253.2.Subspaces1353.3.LinearCombinations1423.4.SubspacesAssociatedwithMatricesandOperators1523.5.BasesandDimension1603.6.LinearSystemsRevisi

4、ted1663.7.*ChangeofBasisandLinearOperators17434CONTENTS3.8.*ComputationalNotesandProjects178Review182Chapter4.GEOMETRICALASPECTSOFSTANDARDSPACES1854.1.StandardNormandInnerProduct1854.2.ApplicationsofNormsandInnerProducts1924.3.UnitaryandOrthogonalMatrices2024.4.*ComputationalNotesa

5、ndProjects210Review212Chapter5.THEEIGENVALUEPROBLEM2135.1.DefinitionsandBasicProperties2135.2.SimilarityandDiagonalization2235.3.ApplicationstoDiscreteDynamicalSystems2325.4.OrthogonalDiagonalization2405.5.*SchurFormandApplications2445.6.*TheSingularValueDecomposition2475.7.*Computa

6、tionalNotesandProjects250Review259Chapter6.GEOMETRICALASPECTSOFABSTRACTSPACES2616.1.NormedLinearSpaces2616.2.InnerProductSpaces2666.3.Gram-SchmidtAlgorithm2766.4.LinearSystemsRevisited2866.5.*OperatorNorms2956.6.*ComputationalNotesandProjects299Review306AppendixA.TableofSymbols307A

7、ppendixB.SolutionstoSelectedExercises309Bibliography323Index325PrefaceThisbookisaboutmatrixandlinearalgebra,andtheirapplications.Formanystudentsthetoolsofmatrixandlinearalgebrawillbeasfundamentalintheirprofessionalworkasthetoolsofcalculus;thusitisimportanttoensurethatstudentsapprec

8、iatetheutilityandbeautyoft