(ii)(AA )=AA AA =(AA A)A =AA AA是幂等矩阵 rank(A)> rank(Aa )2 rank(AA A) rank(a)-trank (A)=rank(AA) (i)x=0→(a4)(xA)(4)=0=4 元≠0→(4)(4A)(4)=(x九)A4A n→A为几4的广义逆矩阵 (iv)BtAS B=SATT S SAT=SAA AT =SAT=B→T-1As是B的广义逆矩阵− − − ii AA = AA AA 2 ( ) ( ) ( ) ( ) − rank A  rank AA AA− 是幂等矩阵 (A)( A )(A) − − (iii)  = 0  − A − 为A的广义逆矩阵 − − = (AA A)A − = AA rank(AA A) −  = rank(A) ( ) ( ) − rank A = rank AA = 0 = A   0 (A)( A )(A) − − AA A − − = (  ) = A iv BT A S B 1 1 ( ) − − − SAA AT − = = SAT = B T −1 A − S −1 是B的广义逆矩阵； SATT A S SAT −1 − −1 =