(6)若A~B,则A=B; ( P-lAP=B,:B=PAP=P-AP=A. (7)若A~B,则4~B" (∵PAP=B, B"=PAP·PP…PAP=PA"P,) (8)若A~B,则A-1~B-1; (∵PAP=B,∴B=PAP) (9)若A~B,则f(4)~f(B),其中为多项式函数 (10)若A~B,则A与B的特征值相同; K(6) 若A ~ B,则A = B; ( , 1 P AP = B −  .) 1 1  B = P AP = P A P = A − − (7) ~ , ~ ; m m 若A B 则A B ( , 1 P AP = B −  B P AP P AP P AP m −1 −1 −1  =   .) 1 P A P − m = (8) ~ , ~ ; −1 −1 若A B 则A B ( , 1 P AP = B −  .) 1 1 1 B P A P − − −  = (9) 若A ~ B,则f (A) ~ f (B),其中f为多项式函数; (10) 若A ~ B,则A与B的特征值相同;