设A为n阶实对称矩阵，P为n阶可逆矩阵，设n维向量a是A的属于特征值λ的特征向量，则(P-1AP)T的属于特征值λ的特征向量是( )
A．P-1a
B．PTa
C．Pa
D．(P-1)Ta
参考答案：B
解析：[详解] (P-1AP)T=PTAT(PT)-1=PTA(PT)-1，由Aα=λα，得PTAα=λPTα，从而pTA(PT)-1pTα=λPTα或者(P-1AP)TPTα=λPTα，于是(P-1AP)T的属于特征值λ的特征向量为PTα，选(B)．
| 阅读下面短文，根据短文内容完成表格中所缺信息。（每空一词） | |||||||||||||
| In Europe many people died during the Second World War. So at the end of the war, there were many children who lost their parents. A man called Hermann Gmeiner wanted to help these children. His idea was simple. He wanted the children who had no parents to have a home. He wanted them to have the deep love and good care of parents. Gmeiner had no enough money, so he asked the people to give him some money. With this money he built the first SOS Children's Village at last, in Australia. It was open in 1949.This is how the SOS Children's Village started. The letters SOS come from "Save our Souls." The words mean "Please help us!" An SOS Children's Village can give help to the children who need help. Hermann Gemeiner's idea for helping orphans soon spread (传播) all over the world. By 1983 there were 17 SOS Children's Villages in the world. Now China has also built many SOS Children's Villages. More and more people like to do something to show their love to the children in the SOS Children's Villages. Do you want to visit an SOS village someday? | |||||||||||||
|