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1、ABSTRACTMatrixtheorieshasbeeninasignificantpositionwhenwecomestoscienceresearchandspecificpractice.ThispaperistostudythetheoryfortheSchurcom-plementofmatriceswhichisoneoftheimportantpartsofmatrixtheories.AndtheSchurcomplementplaysanimportantroleinmanymathemat
2、icalproblems,particularlyinmatrixanalysis,statisticsandnumericalanalysis.ManydomesticandforeignscholarshavemadeagreatofresearchontheSchurcomplementofmatrices.Inthispaper,applyingthepropertiesofSchurcomple-ment,utilizingsomeinequalitytechniques,somenewestima
3、tesofthediagonallydominantdegreeontheSchurcomplementofdiagonallydominantmatricesareobtained,whichimprovesomerelativeresults.Further,asapplicationsofthesederivedresults,wepresentsomedistributionfortheeigenvaluesoftheSchurcom-plementandnewboundsofthedetermina
4、ntofdiagonallydominantmatrices.Inchapterone,wefirstintroducesomebackgroundknowledgeandrecentworksfortheSchurcomplement.Thenwegivesomebasicsymbolsanddefinitionsusedinourpaper.Inchaptertwo,bycombiningwiththecriterionofHmatrixandconstructingthesuitableHmatrix,ap
5、plyingsometechniquesofinequalities,wegetseveralnewestimationsofdiagonallydominantdegree,diagonallydominantdegreeandprod-uctdiagonallydominantdegree,respectively.Moreover,weusetheestimationsofthedeterminantsofthediagonallydominantmatricesandemployinequalitie
6、stechniquestoextendsomeexistingresults.Andsomenumericalexamplesaregiventoverifytheireffectiveness.Inchapterthree,weobtainsomenewestimationsofboundsfortheeigenvaluesofthediagonallydominantmatricesbyusingtheOstrowskiTheorem.Accordingtomanynumericalexamples,wef
7、urtherexplaintheresultsinourpaperissuperiortotheformer.Keywords:diagonallydominantmatrix;Schurcomplement;diagonallydominantdegree;determinant;eigenvalue.II目录摘要....................................................................IABSTRACT.....................
8、.......................................II第一章绪论.........................................................1§1.1背景.........................................................1§1.2本文的主要工作......................
