Re: st: Problems with matrix multiplication and syminv

["G. Anderson" <ga274@cam.ac.uk>]

Hi,

I was using invsym on Stata- just used mata to check the rank.

I thought by construction the outer product, X'X is positive definite?

What I don't understand is why when X is of full rank I get rank deficient 
X'X- this seems to be the source of the problem to me. Could there be some 
rounding error going on with the matrix multiplication or something else 
perhaps?

Thanks,

Gareth

On Jun 14 2013, Sergiy Radyakin wrote:

> Dear Gareth,
> it might be full rank, but is it positive definite? See help for
> invsym(M), as I assume you mean invsym() not syminv() as you typed.
> In general you don't get a row of zeroes:
>
> mata
> :  X=1,2\3,4
> : op=X'X
> : iop=invsym(outerproduct)
>
>
> Best, Sergiy Radyakin
>
> On Thu, Jun 13, 2013 at 7:51 PM, G. Anderson <ga274@cam.ac.uk> wrote:
> > Hi,
> >
> > I am having problems with matrix multiplication and inverting matrices 
> > using Stata.
> >
> > I want to compute the inverse of the outer product of a matrix of 
> > variables, X Note that a lot of the values of X are zero-not sure if 
> > this is problematic)
> >
> > so
> >
> > matrix outerproduct=X'X
> > matrix invouterproduct=syminv(outerproduct)
> >
> > The problem is when I calculate the syminv, I always get a row of 
> > zeros. It seems when I change the data, the location of this row of 
> > zeros changes.
> >
> >
> > A quick check of the rank of X using mata shows it is of full rank 
> > (47), but the rank of outerproduct is only 46- I'm not sure why i get 
> > this result but suspect it has something to do with the fact that I get 
> > a row of zeros.
> >
> > Any ideas?
> >
> >
> > Thanks,
> >
> > Gareth
> >
> >
> >
> >
> >
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