       Re: covariance, eigenvalues

• To: mathgroup at smc.vnet.net
• Subject: [mg51893] Re: covariance, eigenvalues
• From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
• Date: Thu, 4 Nov 2004 01:50:39 -0500 (EST)
• References: <cma08u\$8rl\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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 yahoo.com> wrote in message
news:cma08u\$8rl\$1 at smc.vnet.net...
> 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
>

```

• Prev by Date: Re: How to force Mathematica to treat a number as positive and real?
• Next by Date: Re: Re: Hide Mathematica kernel window
• Previous by thread: Re: covariance, eigenvalues
• Next by thread: Re: covariance, eigenvalues