设a1,a2为n维列向量,A为n阶正交矩阵,证明[Aa1,Aa2]=[a1,a2]
问题描述:
设a1,a2为n维列向量,A为n阶正交矩阵,证明[Aa1,Aa2]=[a1,a2]
答
因为A为正交矩阵
所以 A^TA=E.
所以
[Aa1,Aa2] = (Aa1)^T(Aa2) = a1^TA^TAa2 = a1^Ta2 = [a1,a2]