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