Question

设a1,a2为n维列向量,A为n阶正交矩阵,证明:(1)[Aa1,Aa2]=[a1,a2] (2){Aa1}={a1}

Answer 1

1、=(Aa1)^T*(Aa2)=(a1)^T*A^T*A*a2=(a1)^T*(a2)=.

2、取a2＝a1,由1有||Aa1||^2=||a1||^2.开方得结论.