Question

老师您好,请问“如果A与B相似,C与D相似,证明（AO,OC)与（BO,OD）相似”,怎么证明啊

Answer 1

由已知, 存在可逆矩阵 P,Q 满足 P^-1AP = B, Q^-1CQ = D

令 H =

P 0

0 Q

则 H^-1 =

P^-1 0

0 Q^-1

且 H^-1 [ A 0; 0 C] H = [B 0; 0 D]