[R] find all unit vectors which are orthogonal to a given vector

[peter dalgaard]

> On 30 Oct 2015, at 00:03 , Duncan Murdoch <murdoch.duncan at gmail.com> wrote:
> 
> On 29/10/2015 6:38 PM, Marco Inacio wrote:
>> Is there a function in R to get the set of all unit vectors which are 
>> orthogonal to a given vector?
> 
> No.

Building blocks should be there, though. The last n-1 columns of 

Q <- qr.Q(qr(cbind(v, diag(nrow=length(v))))) 

looks like a good start. 

The full set is an n-1 dimensional sphere in n-space, spanned by those column vectors. If you need more than that representation, some further assembly is required.

-pd

 

> 
> Duncan Murdoch
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
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Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com