MathGroup Archive 2003

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Are points co-planar in (numDimensions-1)?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43283] Re: Are points co-planar in (numDimensions-1)?
  • From: Olaf Rogalsky <Olaf.Rogalsky at physik.uni-erlangen.de>
  • Date: Sat, 23 Aug 2003 08:09:12 -0400 (EDT)
  • Organization: University of Erlangen, Germany
  • References: <bi195e$akp$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

AngleWyrm wrote:
> 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 don't agree. This is the definition of linear independence of n vectors, not of coplanarity. 
A set of k vectors {a_i in Vn | i=1..k} in a n-dimensional vector space Vn are said to be coplanar, 
if all k vectors {a_i in Vn | i=1..k} are elements of a (n-1)-dimensional affine subspace U of Vn.

It is easy to show, that if n==k, any set of vectors {a_i in Vn | i=1..n} is coplanar.

> 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} ]
You have to specify a set of variables to solve for:      ^^^^^^

Solve[ Sum[ k\_i sample[[i]], {i, numDimensions} ] ==0, Table[k\_i,{i,1,numDimensions}] ]



-- 
+----------------------------------------------------------------------+
I Dr. Olaf Rogalsky                         Institut f. Theo. Physik I I
I Tel.: 09131 8528440                       Univ. Erlangen-Nuernberg   I
I Fax.: 09131 8528444                       Staudtstrasse 7 B3         I
I rogalsky at theorie1.physik.uni-erlangen.de  D-91058 Erlangen           I
+----------------------------------------------------------------------+


  • Prev by Date: Re: Timing of Table
  • Next by Date: Re: Fills in StackGraphics ?
  • Previous by thread: Re: Are points co-planar in (numDimensions-1)?
  • Next by thread: RE: Re: Are points co-planar in (numDimensions-1)?