求证:对称正定阵A是正交阵 则A是单位阵
收藏:
0
点赞数:
0
评论数:
0
1个回答

A = P diag(a1,...,an) P'

I = AA'= P diag(...) P' P diag(...) P'

= P diag( a1^2 ,...,an^2 ) P'

diag( a1^2,...,an^2 ) = P'IP = I

又 ai > 0

所以 ai = 1

A = I

=======补充

ai = 1之后,A = P I P' = PP' = I

点赞数:
0
评论数:
0
关注公众号
一起学习,一起涨知识