矩陣跡的不等式及其應用.pdf

1、目錄m^i躲1l.i本文的基本概念及主要工作11.2本文所用的有關數(shù)學符號21.3本文所用的有關引理3第二章關于矩陣和的控制不等式72.1弓I72.2主要結果72.3本章小結7第三章Neumann跡不等式133.1弓|胃133.2Neumann跡不等式133.3本章小結13第四章矩陣Hadamard乘積174.1弓I174.2主要結果174.3本章小結21第五章矩陣乘積之跡的不等式225.1弓|22

2、5.2主要結果225.3本章小結22第六章矩陣跡不等式的應用286.1弓I286.2矩陣逼近306.3本章小結30第七章全文總結與展望317.1全文總結317.2需要進一歩研究的問題31##5：獻32^Mm介35mm36AbstractMatrixTraceInequalityisoneofthemainsubjectsofmatrixtheymanyofvolumeofcalculationwilleventu

3、allyattributedtothematrixtraceoperat.Asamathematicsinstrumentcontrolinequalitiescanusuallydescribemuchinternalrelationshipbetweenmathematicalquantitiesalmostperatetoeverymathematicaldomaindisplayanexcellentrole.Frobenius

4、nmisatypicalunitarilyinvariantnmitistheprimarymeansofresearchingleastsquaressolutionsmatrixperturbation.Hadamardproductisaspecialmatrixmultiplicationithastheimptantapplicationincombinatialschemeofcombinatialtheyacteristi

5、cfunctionofprobabilitytheycommunicationengineeringsoon.Thispaperisdividedinto6sections.FirstsectionisanoverviewofLemmasymbolsSecondsectiondealswithacteristicvaluesingularvalueofcomplexmatrixHermitematrixundercertaincondi

6、tionscontrolinequalitiesnminequalitieswerestudiedatthesametimewldrenownedNeumanninequalitieshasbeenintroduceddiscussedinthirdparttwosingularvalueinequalitiesaboutthetraceofHadamardmatrixwasintroducedinthefollowingsection

7、thenweintroducedtheinequalitiesoftracesofseveralcomplexmatrixcontinuallymultiplyproduct.ByusingacteristicvaluesthepropertyofsingularvaluewegotmcomplexmatrixproductsaswellasinequalitiesofHemitesemidefinitematrixevenpowerp

8、roductsinpartfiveatlastinsectionsixtheapplicationoftracesofmatrixinmatrixapproximationinundertheapproximationthey.Keywds:Characteristicvaluesingularvalueshermitematrix，unitarymatrixfrobeniusnmspositivedefinitematrixsemid