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时间:2020-01-19
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1、.....线性代数发展简介中文版英文版ONTHEHISTORYOFDETERMINANTSByG.A.MILLER,UniversityofIllinoisThehistoryofdeterminantsisanunusuallyinterestingpartofthehistoryofelementarymathematicsinviewofthefactthatitillustratesveryclearlysomeofthedifficultiesinthishistorywhichresultfromtheuseoftechnicaltermsthereinwithoutex
2、hibitingthedefinitemeaningwhichistobegiventotheseterms.Manymodernwritershavebasedtheirdefinitionsofadetermi-nantontheexistenceofasquarematrix.Thiswasdone,forinstance,inthewidelyusedWeber-WellsteinEncyklopadiederElementarmathematik,volume1,4thedition,1922,page304.Fromthispointofviewadeterminantd
3、oesnotexistwithoutitssquarematrix,and,judgingfrommanyofthetextbooksonelementarymathematics,itislikelythatmanystudentsconsiderthesquarematrixasanessentialpartofadeterminant,sothatthetermdeterminantconveystothemadualconceptcomposedofasquarematrixandacertainpolynomialassociatedtherewith.Whentheysp
4、eakoftherowsandcolumnsofadeterminanttheynaturallyarethinkingofitsmatrixandwhentheyspeakofthevaluethereoftheyarenaturallythinkingofthepolynomialimpliedbythetermdeterminant.Whenastudentwhoisfamiliarwithnodefinitionofthetermdeterminantexceptthedualonenotedintheprecedingparagraphmeetswiththecommons
5、tatementthatthediscoveryofdeterminantsisusuallyascribedtoG.W.Leibniz,henaturallyconcludesthatasquarematrixandapolynomialwereassociatedbyG.W.Leibnizinaboutthesamewayastheyareassociatedatthepresenttime.Thisis,however,notthecase.InfactG.W.Leibnizassoci-atedapolynomialwithtwosquarematricesandhederi
6、vedthispolynomialtherefrominawaywhichdifferswidelyfromtheonenowfollowedinexpandingadeterminant.HencethequestionariseswhetheritisdesirabletoassociatethenameofG.W.Leibnizwiththediscoveryofdeterminants.Tothrowsomelightonthisquestionitmaybedesirabletoconsiderherethemotiveswhichledtosomeoftheearlyde
7、velopmentswhicharenowcommonlyas-sociatedwiththebeginningsofthetheoryofdeterminants.Thethreesubjectswhicharecommonlyassociatedwiththeearlyhistoryofdeterminantsare:Thesolutionofasystemofnlinearequationsinnunknowns,theeliminationofth
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