矩陣跡的不等式及其應(yīng)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(guān)數(shù)學(xué)符號(hào)21.3本文所用的有關(guān)引理3第二章關(guān)于矩陣和的控制不等式72.1弓I72.2主要結(jié)果72.3本章小結(jié)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(jié)13第四章矩陣Hadamard乘積174.1弓I174.2主要結(jié)果174.3本章小結(jié)21第五章矩陣乘積之跡的不等式225.1弓|22

2、5.2主要結(jié)果225.3本章小結(jié)22第六章矩陣跡不等式的應(yīng)用286.1弓I286.2矩陣逼近306.3本章小結(jié)30第七章全文總結(jié)與展望317.1全文總結(jié)317.2需要進(jìn)一歩研究的問題31##5：獻(xiàn)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