Re: Are points co-planar in (numDimensions-1)?
- To: mathgroup at smc.vnet.net
- Subject: [mg43240] Re: Are points co-planar in (numDimensions-1)?
- From: "AngleWyrm" <no_spam_anglewyrm at hotmail.com>
- Date: Wed, 20 Aug 2003 22:26:27 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
My last post on this subject lacked depth, so here's more info.
Given some n-dimensional vectors, are they coplanar in n-1? Let a1, a2, ..., an be vectors. If they
are coplanar, then there exists a set of coefficients {k1, k2, ..., kn}, not all zero, which satisfy
the equation:
k1 a1 + k2 a2 + ... + kn an = 0.
I have a dataset I wish to test for this property in various dimensions:
numDimensions = 2;
dataSet = ReadList["data.txt", Number ];
dataSet = Partition[ dataSet, numDimensions ];
At this point I have a set of 2D vectors, and if I take any two of them they HAVE to be coplanar,
right?
sample = Take[ dataSet, numDimensions];
Sum[ k\_i sample[[i]], {i, numDimensions} ] (I've used \_ to indicate subscript here)
Now my problem is in solving for zero on the last equation. I've tried like so:
Solve[ Sum[ k\_i sample[[i]], {i, numDimensions} ] ==0, {k\_i} ]
but it gives an empty set every time. Thanks for any help.
-Jonathan