Question

如果A为n阶正交矩阵,且det(A)=-1,则det(A'-A*)=

Answer 1

因为裤竖信A为正交矩阵
所胡轮以 AA'=E
所以 A^-1 = A'
所纤闹以 det(A'-A*)
= det(A^-1-det(A)A^-1)
= det(2A^-1)
= 2^n det(A^-1)
= 2^n det(A)^-1
= -2^n.