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Re: st: Problems with matrix multiplication and syminv


From   Sergiy Radyakin <serjradyakin@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Problems with matrix multiplication and syminv
Date   Thu, 13 Jun 2013 20:28:10 -0400

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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