[R] A question on orthogonal basis vectors

[kjetil brinchmann halvorsen]

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: jfox at mcmaster.ca
> phone: 905-525-9140x23604
> web: www.socsci.mcmaster.ca/jfox
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help