[Fwd: Confusion regarding the EigenDecomposition class]

[Ron Boisvert <boisvert@nist.gov>]

-------- 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.