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

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karl

Posts: 398
Registered: 8/11/06
Re: Does this matrix function have real eigenvalues?
Posted: Jul 28, 2012 12:24 AM
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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




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