Re: Help-gsl Digest, Vol 229, Issue 1

[Brorson, Stuart]

I looked at your two matrices of eigenvectors.  Thank you for sending them.

Upon my investigation, I found that the column vectors (the eigenvectors) which 
look different are actually scalar multiples of each other.  However, since you 
are dealing with complex eigenvectors, the multiple is not +/-1, but is rather 
a phase, exp(i*phi).

I suggest you form ratios of each of the column pairs (column i from C++ and 
column i from Python) and observe that the ratio is the same for all elements.  
That says each column vector is just a scalar multiple of the other one, and 
both are valid eigenvectors.  In fact, they are the same set of eigenvectors, 
except they can differ by a phase factor.

Best regards,
Stuart Brorson
Northeastern University
Boston, Mass



________________________________
From: Jiasen Guo <jiasenguo1993@gmail.com>
Sent: Friday, January 5, 2024 10:59 AM
To: Brorson, Stuart <s.brorson@northeastern.edu>
Subject: Re: Help-gsl Digest, Vol 229, Issue 1

Hi,
Thanks for the reply. The eigenvectors are not just differed by a sign 
actually. I am attaching the two eigenvector matrixes here. Thanks for your 
kind help.

BTW, does my reply to a specific person open to all the subscribers?

Best,
Jiasen
r