IGG=A +(En -A A)V+W(Em-AA ) VV,W∈ Cmic A1 定理3设A∈CmM,∈C,则 ()(42)=(4),(42)=(A)f (i)AA与AA都是幂等矩阵且 rank(a)=rank (aa)=rank(a 1){ | ( ) ( ), − − − G G = A + En − A A V +W Em − AA , } n m V W C     A{1} T T H H (i) (A ) (A ) , (A ) (A ) − − − − = = 定理3 设 AC mn ,  C,则 (i i) AA− 与A − A都是幂等矩阵,且 rank(A) rank(AA ) rank(A A) − − = =