[R] A question on orthogonal basis vectors

John Fox jfox at mcmaster.ca
Wed Aug 13 16:50:00 CEST 2003

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.

I hope that this helps,

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.

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

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