svd and eigh

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svd and eigh

wilson-4
I am trying out the eigenvectors related  functions in numpy.linalg.I
came across some portions where i have doubts.
1).
i have an array X
if i calculate L=dot(X,X.transpose())
can L be called the covariance matrix of X?I read so in a paper by
Turk&Pentland(equation 3 i think)
can someone clarify this ?

2).
i tried to find eigenvectors using svd() and eigh() functions
evects1,evals,vt=svd(L,0)

evals,evects2=eigh(L)

and sorted both evects1 and evects2 in the descending order of their
evals
here i find that evects1 and evects2 have same values but some of the
values differ in their signs.why is this?

can anyone explain
tia
W
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Re: svd and eigh

Nils Wagner-2
On Fri, 2 May 2008 23:34:19 -0700 (PDT)
  wilson <[hidden email]> wrote:

> I am trying out the eigenvectors related  functions in
>numpy.linalg.I
> came across some portions where i have doubts.
> 1).
> i have an array X
> if i calculate L=dot(X,X.transpose())
> can L be called the covariance matrix of X?I read so in
>a paper by
> Turk&Pentland(equation 3 i think)
> can someone clarify this ?
>
> 2).
> i tried to find eigenvectors using svd() and eigh()
>functions
> evects1,evals,vt=svd(L,0)
>
> evals,evects2=eigh(L)
>
> and sorted both evects1 and evects2 in the descending
>order of their
> evals
> here i find that evects1 and evects2 have same values
>but some of the
> values differ in their signs.why is this?
>
> can anyone explain
> tia
> W
> _______________________________________________
> Numpy-discussion mailing list
> [hidden email]
> http://projects.scipy.org/mailman/listinfo/numpy-discussion


http://en.wikipedia.org/wiki/Singular_value_decomposition
http://en.wikipedia.org/wiki/Eigenvector
http://en.wikipedia.org/wiki/Covariance_matrix


HTH,

       Nils
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Re: svd and eigh

wilson-4
thanks for the links..
but why the different signs for entries in eigenvectors? is it a
library specific thing? shouldn't they be identical?
W
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Re: svd and eigh

Matthieu Brucher-2
Hi,

The opposite of an eigenvector is an eigenvector as well, with the same eigenvalue. Depending on the algorithm, both can be returned.

Matthieu

2008/5/3 wilson <[hidden email]>:
thanks for the links..
but why the different signs for entries in eigenvectors? is it a
library specific thing? shouldn't they be identical?
W
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