# When is it reasonable to assume that the covariance matrix is positive definite?

I know that any covariance matrix must be positive semi-definite, but are there any regimes where it is reasonable to assume that covariance matrix is postive definite.

I want to use this to be able to assume that the covariance matrix is invertible, and use the full matrix in a $$\chi^{2}$$-fit and the Backus-Gilbert method both requiring invertability/positive definite.