代數(shù)特征值反問題.pdf

1、哈爾濱工業(yè)大學碩士學位論文代數(shù)特征值反問題姓名：宋興軍申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：游宏20050701竺璽鎏三些查蘭翌蘭2土蘭竺蘭i：三AbstractAlgebraicinverseeigenvalueproblemsiSthat：UndersomeconditionsseeksomematrixwhichhastheeigenvectorandeigenvaluebeforehandThisissuehaswideap

2、plicationsinengineeringandtechnologySincel956，ACDowningandASHouseholderhavepublishedthefirstarticleaboutthisissuetherearemoreandmorepersonswhodiveintoitsstudymoreandmoregoodresultshavebeengotteninlast50yearsThesourceofal

3、gebraicinverseeigenvalueproblemsisverywideIt’snotonlyinthediscreteinversemathematicsandphysics，butalsoinsolidmechanics，particlephysics，quantummechanics，structuraldesign，autocontrolandSOonBasedonthedifferentconditionanddi

4、fferentbackgroundofapplication，algebraicinverseeigenvalueproblemshavevariousfoFinsThustherearevariousmethodtesolvecorrespondingproblemBecauseofcomplicaeyitselCthereisnotperfectmethodSOfarThestudyaspectaboutthisissuehasto

5、wpartsODesideiSthesolubilityofthisproblemandtheconditionofexistsolutionforthisproblem；ontheotherhand，byrestricttheareaofsolution，theystudythesolubilityofthisproblemandtheconditionofexistsolutionforthisproblemandtheexpres

6、sionofsolution，thatis，requestthesolutiontobesomespecialmatrix，SOastomaketheformofsolutionperfectlyorgettheexclusivesolution，whatisthedemandoffactapplicationThesymmetricandskewanti—symmetricmatrixisveryimportantmatrixinth

7、eengineeringtechnique，theresearchabouttheeveryaspectofthismatrixhasalreadyhadalotofgoodresults，butalgebraicinverseeigenvalueproblemsconcerntoitdidn’tyetseestudyuptonowInthisarticle，wefirstsummarizedthedevelopmentofthealg

8、ebraicinverseeigenvalueproblemsMainlyfocusonthevariousform，studymethodandimportantresultAndthenweenumeratedsomeunresolvedproblemAtlastwebroughtforwardaquestionaboutspecialmatrixinverseproblem，andthenwegottheexpressionofs