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1、大连交通大学2014届本科生毕业设计（论文）外文翻译ThecyclicnatureofthematrixdiagonalizationmethodtofindamatrixFrom:http://books.google.com.hk/books?hl=zh-CN&id=7z5HPgAACAAJAuthor：DavidC.LayMay1990Diagonalmatrixisakindofsimplematrix,whichasquantummechanics,radio,electronicsandinformationengineering,compute
2、rplaysanimportantroleinmanyfields.Matrixdiagonalizationofgreatpracticalvalue.Thispaperdescribestheuseofnature'scyclelookingmatrixdiagonalizationmatrixmethod.ThebasicdefinitionofthetextinvolvedDefinition1:LetAisasquarematrixofordern,ifthereisanonzeronumberandn-dimensionalvector,maki
3、ngiscalledaneigenvalueofthematrixA,isA’safeaturevectorbelongstooneofthe.Definition2:LetAisthen-ordersquare,knownthedeterminantAsthecharacteristicpolynomialofA,denoted,and=0iscalledAcharacteristicequation.Definition3:Then-ordersquareAiscalledreversible,iftherearen-ordermatrixB,sucht
4、hat,whereIistheidentitymatrixofordern.Definition4:A,Bisamatrixofordern,n-orderreversibleifthereexistsamatrixP,sothat,thenAandBaresimilar,calledBofAsimilarmatrix.Definition5:IfthenumberofdomainP,ontheexistenceofann-levelmatrixAinvertiblematrixT,makeasdiagonalmatrix,wecalledmatrixAov
5、eranumberfieldPdiagonalizable;WhenAkeratosiswhencanwesaythattheAdiagonalization,referringtoseekreversiblematrixTsofortheangularmatrix.ManinvolvedinfundamentaltheoremTheorem1:NordermatrixAnecessaryandsufficientconditionsimilartoa11大连交通大学2014届本科生毕业设计（论文）外文翻译diagonalmatrixAbynlinearly
6、independenteigenvectors,andwhenAissimilartoadiagonalmatrixwhen’smaindiagonalelementsarealleigenvalues.Corollary1:MatrixAnecessaryandsufficientconditionsimilartoadiagonalmatrixofeigenvaluesbelongingtoeachoflinearlyindependenteigenvectorsAnumberexactlyequaltothemultiplicityoftheeigen
7、values.Theorem2:IfthematrixAofordernhasnmutuallydifferenteigenvalues(ieeigenvaluesofAaresinglecharacteristicvalue),thenAwillbesimilartoadiagonalmatrix.Thecyclicnatureofthematrixdiagonalizationmethodtofindamatrix1.AbasicsimilarityinthroughthebackdiagonalmatrixnmatrixPthroughthebackc
8、alledabasicarray.itmeetson
