Maths & Stats - Matrix Analysis And Applied Linear Algebra (With Solutions) - Carl Meyer

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1、PrefaceScaffoldingReactingtocriticismconcerningthelackofmotivationinhiswritings,Gaussremarkedthatarchitectsofgreatcathedralsdonotobscurethebeautyoftheirworkbyleavingthescaffoldinginplaceaftertheconstructionhasbeencompleted.Hisphilosophyepitomizedthefor

2、malpresentationandteachingofmathematicsthroughoutthenineteenthandtwentiethcenturies,anditisstillcommonlyfoundinmid-to-upper-levelmathematicstextbooks.Theinherentef-ficiencyandnaturalbeautyofmathematicsarecompromisedbystrayingtoofarfromGauss’sviewpoint.

3、But,aswithmostthingsinlife,appreciationisgen-erallyprecededbysomeunderstandingseasonedwithabitofmaturity,andinmathematicsthiscomesfromseeingsomeofthescaffolding.Purpose,Gap,andChallengeThepurposeofthistextistopresentthecontemporarytheoryandapplica-tion

4、soflinearalgebratouniversitystudentsstudyingmathematics,engineering,orappliedscienceatthepostcalculuslevel.Becauselinearalgebraisusuallyen-counteredbetweenbasicproblemsolvingcoursessuchascalculusordifferentialequationsandmoreadvancedcoursesthatrequires

5、tudentstocopewithmathe-maticalrigors,thechallengeinteachingappliedlinearalgebraistoexposesomeofthescaffoldingwhileconditioningstudentstoappreciatetheutilityandbeautyofthesubject.Effectivelymeetingthischallengeandbridgingtheinherentgapsbetweenbasicandmor

6、eadvancedmathematicsareprimarygoalsofthisbook.RigorandFormalismTorevealportionsofthescaffolding,narratives,examples,andsummariesareusedinplaceoftheformaldefinition–theorem–proofdevelopment.Butwhilewell-chosenexamplescanbemoreeffectiveinpromotingunderstan

7、dingthanrigorousproofs,andwhilepreciousclassroomminutescannotbesquanderedontheoreticaldetails,Ibelievethatallscientificallyorientedstudentsshouldbeexposedtosomedegreeofmathematicalthought,logic,andrigor.Andiflogicandrigoraretoresideanywhere,theyhavetob

8、einthetextbook.Soevenwhenlogicandrigorarenottheprimarythrust,theyarealwaysavailable.Formaldefinition–theorem–proofdesignationsarenotused,butdefinitions,theorems,andproofsneverthelessexist,andtheybecomeevidentasastudent’smaturityincreases.Asignifi