) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 证明:G=D(L+U/) - maX ∑|<1<∑l ≠1 =mx∑< ②A为列对角占优阵,则A为行对角占优阵,有 P(-DA< p(Ⅰ-DA)=p(I-DA)<1 证毕数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 证明： ( ) 1 G = D L +U − i i j i i j j i i i i j i a a a a G =         max 1 max 1 1 =   i j ii ij i a a G ② A为列对角占优阵，则A T为行对角占优阵，有 ( ) 1 1 −  − T  I D A ( ) ( ) 1 1 1  − = −  − − T  I D A  I D A ＃证毕