On 13 Aug 2003 at 10:50, John Fox wrote: > Dear Fred, > > If I understand correctly what you want, the answer is not unique. Think > about the 3D case where you start with one vector. (I assume, by the way, > that you mean orthonormal and that you mean unique up to a reflection.) > There are infinitely many pairs of orthonormal basis vectors for the plane > orthogonal to the initial vector. On the other hand, picking an arbitrary > orthonormal basis isn't hard: The Gram-Schmidt method does this, for example.
To add to this, the qr decomposition is really a version of Gram-Schmidt. So if your basis vectors are the columns of X, you can do something like qr.Q(qr(X), complete=TRUE) Kjetil Halvorsen > > I hope that this helps, > John > > At 09:16 AM 8/13/2003 -0500, Feng Zhang wrote: > >Hey, R-listers, > > > >I have a question about determining the orthogonal > >basis vectors. > >In the d-dimensinonal space, if I already know > >the first r orthogonal basis vectors, should I be > >able to determine the remaining d-r orthognal basis > >vectors automatically? > > > >Or the answer is not unique? > > > >Thanks for your attention. > > > >Fred > > ----------------------------------------------------- > John Fox > Department of Sociology > McMaster University > Hamilton, Ontario, Canada L8S 4M4 > email: [EMAIL PROTECTED] > phone: 905-525-9140x23604 > web: www.socsci.mcmaster.ca/jfox > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help