[R] matrix manipulation

[Therneau, Terry M., Ph.D.]

This is as much a mathematics as an R question, in the "this should be easy but I don't 
see it" category.

Assume I have a full rank p by p matrix V  (aside: V = (X'X)^{-1} for a particular setup), 
a p by k matrix B, and I want to complete an orthagonal basis for the space with distance 
function V.  That is, find A such that t(B) %*% V %*% A =0, where A has p rows and p-k 
columns.

With V=identity this is easy. I can do it in 1-2 lines using qr(), lm(), or several other 
tools.  A part of me is quite certain that the general problem isn't more than 3 lines of 
R, but after a day of beating my head on the issue I still don't see it.  Math wise it 
looks like a simple homework problem in a mid level class, but I'm not currently sure that 
I'd pass said class.

If someone could show the way I would be grateful.  Either that or assurance that the 
problem actually IS hard and I'm not as dense as I think.

Terry T.