Getting *unnormalized* eigenvectors of a matrix with a linear algebra subroutine?


by evgenx
Tags: blas subroutine, eigenvectors
evgenx
evgenx is offline
#1
Nov29-12, 04:56 PM
P: 14
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!

Best regards,
Evgeniy
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Bill Simpson
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#2
Nov29-12, 05:37 PM
P: 972
The Eigenvectors returned from WolframAlpha appear to be un-normalized.

http://www.wolframalpha.com/input/?i...%2C+9%7D%7D%5D

Are these acceptable?
AlephZero
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#3
Nov29-12, 08:03 PM
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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
evgenx is offline
#4
Nov30-12, 03:04 AM
P: 14

Getting *unnormalized* eigenvectors of a matrix with a linear algebra subroutine?


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.


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