Solving Problem to Get Unnormalized Eigenvectors in C/Fortran

[evgenx]

Hallo,

I am trying to solve the following problem. I need to get eigenvectors of a matrix. I know that there are many subroutines for that in linear algebra packages, for instance in Lapack there is DSPEV, but they all give normalized eigenvectors, while I need the "original" unnormalized ones. I will very appreciate any idea/point how one can solve this using a standart library/subroutine in C or fortran (to embed it in a code written in C/frotran).
Many thanks!Evgeniy

 

[Bill Simpson]

The Eigenvectors returned from WolframAlpha appear to be un-normalized.

http://www.wolframalpha.com/input/?i=Eigenvectors[{{1,+2,+3},+{4,+5,+6},+{7,+8,+9}}]

Are these acceptable?

 

[AlephZero]

What do you mean by an "unnormalized" eigenvector?

If you multiply a "normalized" vector by any nonzero random number, it becomes an unnormalized vector - but I don't suppose that was what you really wanted to do..

Normalized vectors just have the some nice property. Either the maximum entrry in the vector is +1.0, or $x^Tx = 1$, or $x^TAx = 1$, or whatever method of normalization you choose. Normalization isn't something mysterious and complicated.

 

[evgenx]

Hi All,

Many thanks for your replies !
Concerning the solution with Mathematica it is of course very nice but unfortunatelly I cannot use it. I need a subroutine in C or fortran because I have to embed it in a code (written in C/fortran). Sorry, that I was imprecise in my post concerning the type of solution.

To the question on the "unnormalized" eigenvectors, yes you are right that normalization isn't mysterious :). In fact, I am interested in the
the normalization factor in the case of x^{T}x=1. I thought that if I get the unnormalized eigenvectors, that is, the "raw" eigenvectors obtained after diagonalization of the matrix, I would be able to find the normalization factor for each vector.

 

[alphy]

,

There are a few potential solutions to this problem. One option would be to use a different subroutine in the Lapack library, such as DSYEV, which allows you to specify whether you want normalized or unnormalized eigenvectors. Another option would be to modify the output of the DSPEV subroutine to unnormalize the eigenvectors yourself, using the eigenvalues as scaling factors.
Alternatively, you could write your own subroutine to calculate the eigenvectors using a different method, such as the power method or QR algorithm, which may give you unnormalized eigenvectors by default. However, this would require more effort and expertise in linear algebra.
Overall, it is important to carefully consider the specific needs and constraints of your project before deciding on the best approach for obtaining unnormalized eigenvectors. I hope this helps, and good luck with your research!