简介：Inthispaper,rankfactorizationsandfactorleftprimefactorizationsarestudied.Theauthorsprovethatanypolynomialmatrixwithfullrowrankhasfactorleftprimefactorizations.Andforaclassofpolynomialmatrices,theauthorsgiveanalgorithmtodecidewhethertheyhaverankfactorizationsorfactorleftprimefactorizationsandcomputethesefactorizationsiftheyexist.

简介：TheconceptofFiedlermatriceswasintroducedin[1]byL.StuartandR.Weaver.In[1],theyinvestigatedthefactorizationofFiedlermatrixintoFiedlermatricesandpre-sentedsomeopenquestionsi.e.WhenisaFiedlermatrixfactorizableasaproductofFiedlermatrices?Arethereusefulsufficientconditions?IfaFiedlermatrixisfactorizable,arethefactorsunique?Ifnot,arethedimensionsofthefactorsunique?Inthispaper,we

简介：LetGbeagraphwithvertexsetV(G)andedgesetE(G)andletgandfbetwointeger-valuedfunctionsdefinedonV(G)suchthat2k-1≤g(x)≤f(x)forallx∈V(G).LetHbeasubgraphofGwithmkedges.Inthispaperitisprovedthatevery(mg+m-1,mf-m+1)-graphGhas(g,f)-factorizationsrandomlyκ-orthogonaltoHandshownthattheresultisbestpossible.