On Sat, 25 Feb 2023 at 20:09, Louis Petingi <Louis.Petingi@csi.cuny.edu> wrote:
Thank you for the reply. I am working with the Laplacian matrix of a graph which is the Degree matrix minus the adjacency matrix.
The Laplacian is a symmetric matrix and the smallest eigenvalue is zero. As the rows add it to 0, Lx=0x, and 1 is the resulting vector.

The ones vector is one solution, but so is all 2, or any other vector where all the entries are equal. There is nothing in the eigenvector that makes one more "worthy" than others, except for in particular applications.
 
That is what I meant by the original eigenvector and sorry for the confusion the confusion. Most eigenvalues/eigenvalues calculators will give you 1 for first eigenvector

Sympy does seem to always return a 1 on the last non-zero entry of the vector. Is that the normalisation you are looking for?

Here it is how it is computed, by the way:
https://github.com/sympy/sympy/blob/26f7bdbe3f860e7b4492e102edec2d6b429b5aaf/sympy/polys/matrices/ddm.py#L390-L406


/David.



Best

Louis Petingi
Professor of Computer Science
College of Staten Island
City University of NY
From: Ilhan Polat <ilhanpolat@gmail.com>
Sent: Saturday, February 25, 2023 11:46 AM
To: Discussion of Numerical Python <numpy-discussion@python.org>
Subject: [Numpy-discussion] Re: non normalised eigenvectors
 
Could you elaborate a bit more about what you mean with original eigenvectors? They denote the direction hence you can scale them to any size anyways.

On Sat, Feb 25, 2023 at 5:38 PM <louis.petingi@csi.cuny.edu> wrote:
Dear all,

I am not an expert in NumPy but my undergraduate student is having some issues with the way Numpy returns the normalized eigenvectors corresponding to the eigenvalues. We do understand that an eigenvector is divided by the norm to get the unit eigenvectors, however we do need the original vectors for the purpose of my research. This has been a really frustrated experience as NumPy returns the normalized vectors as a default. I appreciate any suggestions of how to go about this issue. This seems to be a outstanding issue from people using Numpy.

Thanks

LP
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