[SciPy-user] finding approximate rank of matrix

[Dr Seth OLSEN]

Hi Dan,

You should be able to do this with a singular value decomposition.  The
singular values will tell you the projection along each corresponding
vector.  Choose a threshold for the singular value and take the vectors
corresponding to values above that - these should define your subspace.

Cheers,

Seth



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Dr Seth Olsen, PhD
Postdoctoral Fellow, Biomolecular Modeling Group
Centre for Computational Molecular Science
Chemistry Building,
The University of Queensland
Qld 4072, Brisbane, Australia

tel (617) 33653732
fax (617) 33654623
email: s.olsen1 at uq.edu.au
Web: www.ccms.uq.edu.au 

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----- Original Message -----
From: Dan Christensen <jdc at uwo.ca>
Date: Thursday, August 4, 2005 2:51 pm
Subject: [SciPy-user] finding approximate rank of matrix
> Suppose you have 300 vectors each with 64 components, and you want to
> find the smallest subspace of R^64 that they all lie in.  That would
> just be the rank of the 300x64 matrix that they form.  But
> unfortunately the vectors are generated numerically to low precision
> (maybe 1e-5 relative error?).  So taken literally, they will span
> R^64.  I'd like to find the smallest subspace of R^64 that they all
> approximately lie in, with a specified tolerance.
> 
> Is there an easy way to do this?
> 
> Thanks,
> 
> Dan
> 
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