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From Thomas Neidhart <thomas.neidh...@gmail.com>
Subject Re: [math] eigenvector doubts and issues
Date Tue, 12 Nov 2013 21:49:17 GMT
On 11/12/2013 06:31 PM, andrea antonello wrote:
> Hi Thomas,
> 
>> that's exactly what we are looking for, so do not hesitate to ask questions.
> 
> ok, I put together a small set of examples, which for now I put on a
> wiki of the project I am doing this for (since I have access on that
> one): http://code.google.com/p/jgrasstools/wiki/Eigenvectors
> 
> Since in the 3d space I do not get the results I was hoping for, it
> would be great if some expert could give me a hint.
> 
> Let me know what you think.

Hi Andrea,

are you sure that your eigenvectors are drawn correctly?

I tried to reproduce your results with geogebra, and in my case the
plane defined by the two eigenvectors with the least eigenvalue seems to
split the values quite well, see this image:

http://people.apache.org/~tn/pca.png

The results from the computations:

covariance:
  {0.7272727273,0.0,0.1818181818},
  {0.0,0.3409090909,0.2272727273},
  {0.1818181818,0.2272727273,0.2727272727}}

lambda1 =  0.8056498828134406
v1 =  {0.9015723558; 0.1900593782; 0.3886447222}

lambda2 = 0.4874287594020183
v2 = {-0.3799516758; 0.7774478203; 0.5012101464}


lambda3 = 0.04783044869363171
v3 = {-0.2068913033; -0.5995434259; 0.7731388421}

The plane is constructed with v2 and v3.

Thomas

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