Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Does this matrix function have real eigenvalues?
Replies: 9   Last Post: Aug 1, 2012 3:43 AM

Advanced Search
Reply to this Topic Reply to this Topic

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
karl

Posts: 213
Registered: 8/11/06
Re: Does this matrix function have real eigenvalues?
Posted: Jul 28, 2012 12:24 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Am 28.07.2012 04:21, schrieb Paul:
> Let G = I - inv(W) * B where W and B are real symmetric positive
> definite matrices.
> In simulations it appears that G always has real eigenvalues, though G
> is not necessarily symmetric or positive definite.
>
> I wonder if it can be proved in general that G has real eigenvalues?
> Bonus question: Is there a simple relationship between the eigenvalues
> of G and those of W and B?
>
> Best,
> Paul
>

G= inv(W)*(W-B)= inv(W)*W-inv(W)*B=I-inv(W)*B.
Inv(W) and W-B are symmetric, therefore their product will be symmetric too AFAIS.

Karl

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2013. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.