简介：Asignpatternmatrixisamatrixwhoseentriesarefromtheset{+,-,0}.Thesymmetricsignpatternmatricesthatrequireuniqueinertiahaverecentlybeencharacterized.Thepurposeofthispaperistomoregenerallyinvestigatetheinertiasetsofsymmetricsignpatternmatrices.Inparticular,nonnegativefri-diagonalsignpatternsandthesquaresignpatternwithall+entriesareexamined.AnalgorithmisgivenforgeneratingnonnegativerealsymmetricToeplitzmatriceswithzerodiagonalofordersn≥3whichhaveexactlytwonegativeeigenvalues.Theinertiasetofthesquarepatternwithall+off-diagonalentriesandzerodiagonalentriesisthenanalyzed.Thetypesofinertiaswhichcanbeintheinertiasetofanysignpatternarealsoobtainedinthepaper.Specifically,certaincompatibilityandconsecutivenesspropertiesareestablished.

简介：Inqualitativeandcombinatorialmatrixtheory,westudypropertiesofamatrixbasedonqualitativeinformation,suchasthesignsofentriesinthematrix.Amatrixwhoseen-triesarefromtheset{+,-,0}iscalledasignpatternmatrix(orsignpattern).Forare-almatrixB,bysgn(B)wemeanthesignpatternmatrixinwhicheachpositive(respec-tively,negative,zero)entryofBisreplacedby+(respectively,-,0).IfAisann×n