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# Re: st: Problems with matrix multiplication and syminv

 From "G. Anderson" To statalist@hsphsun2.harvard.edu Subject Re: st: Problems with matrix multiplication and syminv Date 14 Jun 2013 01:13:23 +0100

```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)

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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