l****y
发帖数: 267 | 1 【 以下文字转载自 Mathematics 讨论区,原文如下 】
发信人: duz ( duz), 信区: Mathematics
标 题: Re: A question
发信站: Unknown Space - 未名空间 (Thu Oct 16 00:54:55 2003) WWW-POST
If |A|=0, the result is obvious,
otherwise
There's invertible matrix P so that I=P'AP
and
P'(B-A)P is non-negative definite
or
P'BP -I non-negative definite
so for each enginvalue u of P'BP, x is the enginvector, we could get
x'(P'BP-I)x=(u-1)x'x>=0, so u>=1
So |P'BP|>=1
Since |P'BP|=|P'||B||P|
1=|P'AP|=|P'||A||P|
so |B|>=|A|. | a***l
发帖数: 66 | 2 Should add the case where there are zero eigenvalues, though trivial.
【在 l****y 的大作中提到】
: 【 以下文字转载自 Mathematics 讨论区,原文如下 】
: 发信人: duz ( duz), 信区: Mathematics
: 标 题: Re: A question
: 发信站: Unknown Space - 未名空间 (Thu Oct 16 00:54:55 2003) WWW-POST
: If |A|=0, the result is obvious,
: otherwise
: There's invertible matrix P so that I=P'AP
: and
: P'(B-A)P is non-negative definite
: or
| l****y
发帖数: 267 | 3 yes, thanks for your attention to this problem. @_@
【在 a***l 的大作中提到】
: Should add the case where there are zero eigenvalues, though trivial.
| m***t
发帖数: 4509 | 4 人和人的觉悟就是不一样，您老一上来就回答问题，
我天天就看吃的。
【在 a***l 的大作中提到】
: Should add the case where there are zero eigenvalues, though trivial.
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