定理5：给定矩阵A,则 (1)rank 4"=rankA (2)(A)=A (3)(AH)=(A)H,(A)=(A)H (4)(AA)=4(4)(A4)=(4)A (5)A=(AA)A=A(AA) (6)R(A)=R(A),N(A)=N(A) 证：(I)A∈A{L,2}→rank A'=rankA (2)Penrose方程中（①←→(ii,(ii)←→(iv)互为对称 故 (A)=A 7定理 5： 给定矩阵 A，则 (1) rank A+ =rankA (2) ( ) A+ +=A (3) ( ) H A + =( )H A+ , () () T T A A + + = (4) ( ) () H H AA A A ++ + = , ( )() H H AA A A + ++ = (5) () () H HHH A A A A A AA ++ + = = (6) ( ) ( ), ( ) ( ) H H RA RA NA NA + + = = 证：(1) A+ ∈A{1,2} → rank A+ =rankA (2) Penrose 方程中 (i)↔(ii), (iii)↔(iv) 互为对称 故 ( ) A+ +=A. 7