(1)o=R(A), (2)kerσ=N(A)=R(A) AA)Ab=0今(AA)A4b=0分Ab=0, kero=N(A=R(A R"=oV e kero=R(AOR(A) o是R"到R(A)的正交投影 Vb∈kera,有A(AA)Ab=0,r(A)=n 兮(AA)4b=0,分Ab=0,→b∈N(A)6 (2) ker ( ) ( ) , (1) ( ), ⊥ = = = N A R A V R A T   是R 到R(A)的正交投影. m  ⊥ − −  = = =  =  = ker ( ) ( ) ( ) 0 ( ) 0 0, 1 1 N A R A A A A A b A A A b A b T T T T T T  ker ( ) ( ) . ⊥ R = V  = R A  R A m   ( ) 0, 0, ( ) ker , ( ) 0, ( ) 1 1 T T T T T T A A A b A b b N A b A A A A b r A n  =  = →    = = − −  有 