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 >