[R] matrix manipulation -solved

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

Yes it is obvious --- once someone else pointed it out.
Thanks for the hint.

Terry T.


On 07/16/2015 12:52 PM, Peter Langfelder wrote:
> 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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