矩陣數(shù)值特征和跡占優(yōu)矩陣的研究.pdf

1、重慶大學(xué)碩士學(xué)位論文矩陣數(shù)值特征和跡占優(yōu)矩陣的研究姓名：胡興凱申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：伍俊良201004重慶大學(xué)碩士學(xué)位論文英文摘要IIABSTRACTMatrixanalysismatrixcomputationshavewideapplicationsinmathematicphysicscomputationalmathematicscontroltheyimageanalysiseconomicsetc.The

2、purposeofthisthesisistodiscussthenumericalacteristicsofmatricesthepropertiesiterativealgithmoftracedominantmatrices.Themainresultsinnovationsareasfollows:1.Theestimationsflowerboundsftherankofnonnmalmatrixareinvestigated

3、.Threelowerboundsftherankareobtained.InmanycasestheestimationsaremeaccuratethanKyFanHoffmaninequality.2.F()0hAsuchthat()22()1FFhAtrAnAAAAA=????weprovethatalltheeigenvaluesarelocatedinthefollowingdisk()2:trAnhAtrAzCznn???

4、??∈?≤??????Basedonmatrixpartitionsimilaritytransfmationmeaninequalitythedisktheemswhichconcludealltheeigenvaluesareshown.3.SomeimprovementsofBrauertheemKyFantheemarepresentedtheeigenvaluesinclusionregionsaregivenasfollow

5、s11111:nnniijjkikljlklijijkiljijzCzazapapapp===≠≠≠????????∈??≤????????????∑∑∪()()()()1:niijjiiiiiijjijijzCzazaBbBbaaρρ=≠∈??≤???∪Thedistributionsftheeigenvaluesoftensproductofmatricesareobtainedseveralestimationsftherealp

6、artimaginarypartofeigenvaluesareshown.4.Basedonsingularvaluedecompositioninequalitytheiestheupperboundlowerboundfthesingularvalueareobtainedthefollowinginequalityholds()221122nnFFBAdiagτστστσ≤?5.Severalpropertiesoftraced