Stata test for matrix positive definite matrix is ambiguous

[Peter Hoon]

Have completed a successful run of Stata expectation maximization estimation of the covariances of 94 variables. I used _getcovcorr to further examine the matrix, and to check on whether the matrix is positive semi-definite and/or positive definite. The name of my matrix is Cov_em. To test, I issued these commands according to the documentation for _getcovcorr:

_getcovcorr Cov_em, check(psd)
_getcovcorr Cov_em, check(pd)

The result of these commands is simply a dot (period), without any statement or message regarding whether the matrix passed the tests. Thus, the result is ambiguous. Does "nothing" returned except a period mean these tests were passed?

I then issued the command:

matrix list r(C) in case a message was embedded therein. The matrix was correctly listed, but no information was described regarding whether the tests were passed.

I next issued the commands:

matrix symeigen X v = Cov_em
matrix list v

I got 94 eigenvalues printed out; the last, smallest eigenvalue was: .00026395 a positive number

The matrix determinant was a very small number, 9.580 e -95, indeed a very small positive number.

Fellow statisticians, what do we have here? A positive definite matrix? A positive semi-definite matrix?

Pete sends his best regards to all with thanks for your opinions.