Weintroducefourtypesofspecialeigenvalueswhichlieontheboundaryofcertaininclusionregionsforthespectrumofacomplexsquarematrix,i.e.,R_r(G_c)-,O(a)-,B_r(B_c)-.andOB(a)-eigenvalues.Thenwecharacterizetheseeigenvaluesandtheircorrespondingeigenvectorsforirreduciblematrices,Finallywegivesomenewsufficientconditionsforanirreduciblecomplexmatrixtobenonsingular.