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.