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Re: st: Problems with matrix multiplication and syminv


From   "G. Anderson" <ga274@cam.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Problems with matrix multiplication and syminv
Date   14 Jun 2013 09:07:40 +0100

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





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