Re: Are points co-planar in (numDimensions-1)?
- To: mathgroup at smc.vnet.net
- Subject: [mg43289] Re: [mg43237] Are points co-planar in (numDimensions-1)?
- From: Hugh Walker <hwalker at gvtc.com>
- Date: Sat, 23 Aug 2003 08:09:22 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Wednesday, August 20, 2003, at 09:26 PM, AngleWyrm wrote:
> Hi,
> I have a vector generator that produces sets of vectors in
> numDimensions space. It has been said
> that they might be coplanar in numDimensions-1, and I wish to test
> this.
>
> For instance, if the number of dimensions is set at three:
> dataSet=ReadList["data.txt", {Number, Number,Number}]
> Is dataSet coplaner in some 2D plane?
Here is one way:
Construct the numDimensions X numDimensions covariance matrix with the
set of vectors and find its eigenvalues.One zero eigenvalues will
indicate the vectors lie in a space of dimension numDimensions-1: two
zero eogenvectors will indicate the vectors lie in a space of dimension
numDimensions-2; etc.
==========
Hugh Walker
Gnarly Oaks