解题思路:
先分别求出特征值(显然A,B相似矩阵,特征值相同),特征向量,
然后分别施密特正交化,得到相应正交矩阵P1,P2
即P1'AP1=diag = P2'BP2
则P2P1'AP1P2'=B
即得到正交矩阵P=P1P2'
![](https://iknow-pic.cdn.bcebos.com/7af40ad162d9f2d367a3ff24a1ec8a136227cc4f?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
![](https://iknow-pic.cdn.bcebos.com/472309f7905298223af4e208dfca7bcb0b46d432?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
施密特正交化,单位化得到P1=
-1/√2 1/√2
1/√2 1/√2
![](https://iknow-pic.cdn.bcebos.com/8326cffc1e178a82b20ba56bfe03738da877e8c2?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
施密特正交化,单位化得到P2=
-1/√5 2/√5
2/√5 1/√5
P=P1P2'=
-1/√2 1/√2
1/√2 1/√2
*
-1/√5 2/√5
2/√5 1/√5
=
3/√10 -1/√10
1/√10 3/√10