# Re: st: Problem with Cholesky matrix function?

 From May Boggess To statalist@hsphsun2.harvard.edu Subject Re: st: Problem with Cholesky matrix function? Date 24 Nov 2003 08:59:02 -0600

```On Sun, 2003-11-23 at 19:14, Kaleb Michaud wrote:

> symmetric S[10,10]
>        r1   r2   r3   r4   r5   r6   r7   r8   r9  r10
>   c1    1
>   c2    2    2
>   c3    3    3    3
>   c4    4    4    4    4
>   c5    5    5    5    5    5
>   c6    6    6    6    6    6    6
>   c7    7    7    7    7    7    7    7
>   c8    8    8    8    8    8    8    8    8
>   c9    9    9    9    9    9    9    9    9    9
> c10   10   10   10   10   10   10   10   10   10   10
>
> The problem is this:
>
> . matrix C = cholesky(S)
> matrix not positive definite
> r(506);
>

For a matrix to be positive definite it needs to have all positive
eigenvalues. So, Kaleb can check his matrix by using -symeigen- to
compute the eigenvalues of S. I have pasted some code below that does
this.

Out of curiosity I also looked at the matrices that had the same pattern
in the entries as S, but smaller sizes, and found that they had similar
structure to the eigenvalues, that is, they all have one large positive
eigenvalue and the rest negative. The code below will run these cases as
well.

yours,
--May

mboggess@stata.com

matrix S=[1,2,3,4,5,6,7,8,9,10\2,2,3,4,5,6,7,8,9,10\3,3,3,4,5,6,7,8,9,10\ /*
*/4,4,4,4,5,6,7,8,9,10\5,5,5,5,5,6,7,8,9,10\6,6,6,6,6,6,7,8,9,10\ /*
*/ 7,7,7,7,7,7,7,8,9,10\8,8,8,8,8,8,8,8,9,10\9,9,9,9,9,9,9,9,9,10\ /*
*/10,10,10,10,10,10,10,10,10,10]
mat list S
mat symeigen X v = S
mat list v

matrix S=[1,2,3,4,5,6,7,8,9\2,2,3,4,5,6,7,8,9\3,3,3,4,5,6,7,8,9\ /*
*/4,4,4,4,5,6,7,8,9\5,5,5,5,5,6,7,8,9\6,6,6,6,6,6,7,8,9\ /*
*/7,7,7,7,7,7,7,8,9\8,8,8,8,8,8,8,8,9\9,9,9,9,9,9,9,9,9]
mat list S
mat symeigen X v = S
mat list v

matrix S=[1,2,3,4,5,6,7,8\2,2,3,4,5,6,7,8\3,3,3,4,5,6,7,8\ /*
*/4,4,4,4,5,6,7,8\5,5,5,5,5,6,7,8\6,6,6,6,6,6,7,8\ /*
*/7,7,7,7,7,7,7,8\8,8,8,8,8,8,8,8]
mat list S
mat symeigen X v = S
mat list v

matrix S=[1,2,3,4,5,6,7\2,2,3,4,5,6,7\3,3,3,4,5,6,7\ /*
*/4,4,4,4,5,6,7\5,5,5,5,5,6,7\6,6,6,6,6,6,7\ /*
*/7,7,7,7,7,7,7]
mat list S
mat symeigen X v = S
mat list v

matrix S=[1,2,3,4,5,6\2,2,3,4,5,6\3,3,3,4,5,6\ /*
*/4,4,4,4,5,6\5,5,5,5,5,6\6,6,6,6,6,6]
mat list S
mat symeigen X v = S
mat list v

matrix S=[1,2,3,4,5\2,2,3,4,5\3,3,3,4,5\ /*
*/4,4,4,4,5\5,5,5,5,5]
mat list S
mat symeigen X v = S
mat list v

matrix S=[1,2,3,4\2,2,3,4\3,3,3,4\4,4,4,4]
mat list S
mat symeigen X v = S
mat list v

matrix S=[1,2,3\2,2,3\3,3,3]
mat list S
mat symeigen X v = S
mat list v

matrix S=[1,2\2,2]

mat list S
mat symeigen X v = S
mat list v

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```