strictly decresing sample eigenvalues

Question

If we assume that the eigenvalues of covariance matrix are strictly decresing $\lambda_1>\cdots >\lambda_n$.

Under which conditions we can assume the same for the sample eigenvalues, that is, $\hat{\lambda}_1>\cdots >\hat{\lambda}_n$.

Answer 1

Strictly positive definite and unequal (sample) variances.