Verify a matrix is positive semi-definite

[Tamas_Papp]

@Mr.Robot

Then I need to verify in both directions, i.e.

1. Given a positive semidefinite matrix A\mathbf{A}, show that it is a covariance matrix.
2. Given a covariance matrix, show that it is positive semidefinite.

I am not sure I understand the whole context, but this is a well-known property (covariance matrices are psd, and psd matrices are covariance matrices). I don’t know how you could verify a statement about an uncountably infinite set numerically.