# Why does sample covariance matrix inflates the larger eigenvalues and shrinks the smaller eigenvalues of the covariance matrix?

In classification context, using the maximum likelihood, the sample covariance matrix for each class, estimates the larger eigenvalues of the covariance matrix of each class, larger and estimates the smaller eigenvalues smaller. Why is that? I am studying Regularized Discriminant Analysis written by Friedman.

• That sounds interesting. Where did you get this assertion? – Cave Johnson Jun 17 '18 at 10:20
• google.com/… On the third page of this pdf, two paragraphs after equation 13. It says "it is well known" – fof Jun 17 '18 at 10:36