R help - Nov 2009 - question about how to generate an orthogonal matrix with a known vector

Hi,

Sorry that this question may not be related to R directly...but I am trying
to find a nxn orthogonal matrix that can minimize my objective function and
I know values for one of the n columns.  I should only need n(n-1)/2 - (n-1)
independent parameters to represent this orthogonal matrix.  Any good way to
parameterize the matrix?  I really appreciate your help here.

Ted 
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## You can do this with the qr functions.

tmp <- rnorm(4)

tmp.qr <- qr(tmp)

tmp.complete <- qr.Q(tmp.qr, complete=TRUE)

tmp.complete[,1] / tmp