Re: Eigenvalues of a product of matrices?
From: Ruben Hernandez (hernandez_at_NOSPAM.stls.frb.org)
Date: 12/10/04
- Next message: Michael Hosea: "Re: Who uses clapack?"
- Previous message: Victor Eijkhout: "Re: Who uses clapack?"
- In reply to: Peter Spellucci: "Re: Eigenvalues of a product of matrices?"
- Messages sorted by: [ date ] [ thread ]
Date: Fri, 10 Dec 2004 14:14:00 -0600
Thanks,
R.
Peter Spellucci wrote:
> In article <cp7c4j$f8q$1@snews.frb.gov>,
> Ruben Hernandez <hernandez@stls.frb.org> writes:
> >Hello,
> >
> >Suppose W is a square symmetric real matrix of size n by n.
> >D is a diagonal matrix with real elements (d1, ..., dn).
> >Is there an interesting relationship between the eigenvalues
> >of W and the eigenvalues of the product D*W ?
> >
> >Thanks,
> >Ruben.
> >
>
> no.
> the only useful result on eigenvalues of products of matrices which do not
> commute i know of is
>
>
> if A is normal and U is unitary then
> max lambda(A) >= abs(lambda_i(A*U) >= min lambda (A)
> hence this applieshere with D=U if the elements of D all have abs value one
>
> if the two matrices commute then they have a common eigensystem and then the
> property is obvious
> hth
> peter
- Next message: Michael Hosea: "Re: Who uses clapack?"
- Previous message: Victor Eijkhout: "Re: Who uses clapack?"
- In reply to: Peter Spellucci: "Re: Eigenvalues of a product of matrices?"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
