Completion for tight sign-central matrices

A real matrix A is called a sign-central matrix if for,every matrix ~A with the same sign pattern asA, the convex hullof columns of ~A contains the zero vector. A sign-central matrixAis called a tight sign-central matrix if the Hadamard (entrywise)product of any two columns ofA contains a negative component.A real vectorx = (x1;:;x n )T is called stable ifjx1j j x2j j xn j. A tight sign-central matrix is called atightsign-centralmatrixif each of its columns is stable.In this paper, for a matrixB, we characterize those matricesC such that [B;C] is tight (tight) sign-central. We also constructthe matrixC with smallest number of columns among all matricesC such that [B;C] is tightsign-central.