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Re: covariance, eigenvalues

  • To: mathgroup at
  • Subject: [mg51893] Re: covariance, eigenvalues
  • From: "Steve Luttrell" <steve_usenet at>
  • Date: Thu, 4 Nov 2004 01:50:39 -0500 (EST)
  • References: <cma08u$8rl$>
  • Sender: owner-wri-mathgroup at

130 samples of a 15000-dimensional vector are almost certainly far too few 
to estimate the covariance matrix. The exception to this is if the 
15000-dimensional vectors happen to be drawn from a PDF that constrains the 
vectors to live in a very low-dimensional subspace.

Mathematica has plenty of tools to help you do what you want, such as the 
various standard Statistics` packages and the Eigensystem, Eigenvalues, and 
Eigenvectors functions - these functions know how to handle sparse arrays. 
Also you should consider using the SingularValueDecomposition function.

Steve Luttrell

"cagdas" <cagdaskafali at> wrote in message 
news:cma08u$8rl$1 at
> Hi,
> I have a random vector of length 15000 by 1. I have 130 samples of
> this vector and I would like to estimate the covariance matrix. Is
> there a built-in function in mathematica to do that ? If there is, can
> it handle a covariance matrix of size 15000 by 15000?
> If I can get that matrix the next step is an eigenvalue decomposition.
> Are there any built-in functions to compute eigenvalues and
> eigenvectors of a given matrix ? and again, is it possible to use
> these functions for a matrix of size 15000 by 15000?
> I would appreciate any suggestions (related to mathematica or some
> other options)
> Thanks
> Cagdas

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