... if matrix A is square and nonsingular, then A+= A−1 and [ABB∗D] ≥0ifandonlyifD ≥B∗A−1B .Let Z1 and Z2be the real matrices of zeros and ones of order m ×r and n ×s,respec-tively, ... are rectangular partitioned matrices of order m ×n,thendueto (2.11)ofLemma 2.2 there exist two real matrices Z1 and Z2 of zeros and ones of ordermk×r and nk×s, respectively, such thatki=1∗Ai= ... (3.27).Proof. This theorem follows from [3, Theorem 3.1(ii) and (iii)]. We give proof for thesake of convenience. In (2.20 )and( 2.22)ofLemma 2.4,setk= 1andreplaceU by ZT,U∗by Z,andX byki=1ΘAi,whereZ,...