I came across a statement that for the sample covariance matrix is +ve definite with probability one given that the numbre of samples is more than the dimension of the space from which the samples are drawn. It is fairly straightforward to say that independence of the given samples over the given space implies the +ve definiteness. Hence the necessity of the number being more than the dimension would be implies.
However, I am unable to explain cogently how the above statement holds true. I shall appreciate any comments/explanations. Sincerely, Varun firstname.lastname@example.org