[R] matrix manipulation

[Peter Langfelder]

Hi Terry,

maybe I'm missing something, but why not define a matrix BB = V'B;
then t(B) %*% V = t(BB), then your problem reduces to finding A such
that t(BB) %*% A = 0?

Peter

On Thu, Jul 16, 2015 at 10:28 AM, Therneau, Terry M., Ph.D.
<therneau at mayo.edu> wrote:
> 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.
>
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