Re: st: Problems with matrix multiplication and syminv

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

Hi,

Sorry, yes it will be at least positive semi definite.

So do you think that is where the problem lies- that X'X is not positive 
definite?

Thanks,

Gareth

On Jun 14 2013, Sergiy Radyakin wrote:

> no, by construction it is positive semi-definite.
>
> On Thu, Jun 13, 2013 at 8:13 PM, G. Anderson <ga274@cam.ac.uk> wrote:
> > 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
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > *
> > > > *   For searches and help try:
> > > > *   http://www.stata.com/help.cgi?search
> > > > *   http://www.stata.com/support/faqs/resources/statalist-faq/
> > > > *   http://www.ats.ucla.edu/stat/stata/
> > > *
> > > *   For searches and help try:
> > > *   http://www.stata.com/help.cgi?search
> > > *   http://www.stata.com/support/faqs/resources/statalist-faq/
> > > *   http://www.ats.ucla.edu/stat/stata/
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/help.cgi?search
> > *   http://www.stata.com/support/faqs/resources/statalist-faq/
> > *   http://www.ats.ucla.edu/stat/stata/
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/faqs/resources/statalist-faq/
> *   http://www.ats.ucla.edu/stat/stata/
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/