[Fwd: Re: [Fwd: Confusion regarding the EigenDecomposition class]]

[Ron Boisvert <boisvert@nist.gov>]

Sender: "G. W. (Pete) Stewart" <stewart@cs.umd.edu>
Subject: Re: [Fwd: Confusion regarding the EigenDecomposition class]



The problem is that 5 is an eigenvalue of multiplicity 3.  Hence there
is a three dimensional space in which every nonzero vector is an
eigevector corresponding to the eigenvalue 5.  It is not surprising
that two different algorithms should end up with two different sets of
three eigenvectors to span that subspace.  Properly normalized, the
eigenvectors corresponding to the eigenvalue one produced by the two
algorithms should be the same.

Pete Stewart


On Wed, 21 Feb 2007, Ron Boisvert wrote:

> Date: Wed, 21 Feb 2007 10:16:17 -0500 (EST)
> From: Ron Boisvert <boisvert@nist.gov>
> Reply-To: jama@nist.gov
> To: Multiple recipients of list <jama@nist.gov>
> Subject: [Fwd: Confusion regarding the EigenDecomposition class]
>
>
>
>
> -------- Original Message --------
> Subject: 	Confusion regarding the EigenDecomposition class
> Date: 	Tue, 20 Feb 2007 16:33:17 -0500 (EST)
> From: 	Greg Sterijevski <Greg.Sterijevski@InfiniumCM.com>
> Reply-To: 	Greg.Sterijevski@InfiniumCM.com
> To: 	boisvert@nist.gov
>
>
>
> All,
>
> I have been experimenting with the JAMA classes. I noticed something
> which is puzzling to me. Please excuse my ignorance if the answer is
> obvious.
>
> I take the matrix presented below
>
>   {{4, -1, -1, -1}, {-1, 4, -1, -1}, {-1, -1, 4,-1},{-1,-1,-1,4}};
>
> and run it throught the Eigendecomposition class.
>
> It returns eigenvalues which are (.99999999, 4.9999999999, 5.0 , 5.0 ).
> I also get the eigenvectors.
>
> In the Eigendecomposition class, I force the class to take the path of
> the nonSymmetric decomposition. I set issymmetric=false.
>
> I still get the same eigenvalues, but the eigenvectors change radically.
> Furthermore, it does not look like vectors are in the same direction. I
> checked that there are no complex roots. Is this the expected result?
>
> Furthermore, if I form the sandwich product of the original matrix with
> its eigenvectors I do not get the eigenvalues on the diagonal.
>
> Thanks for your help!
>
> -Greg
>
> Greg Sterijevski
>
> PS I tried to look for a bug report/errata page but could not find it.
> PPS This is the second time I am sending this message. It seems like
> your servers are flagging this as spam.
>
> PPS This is the 3^rd time I am sending this. Your spam blocker does not
> like my Hotmail account.
>
>
>