Distinctness of the Eigenvalues of a Quadratic form in a Multivariate Sample
Masashi Okamoto · The Annals of Statistics · 1973
This paper shows that a quadratic form in a multivariate sample has a certain rank and its nonzero eigenvalues are distinct with probability one under the assumption that the matrix defining the quadratic form satisfies a certain rank condition and that the underlying distribution of the sample is absolutely continuous with respect to Lebesgue measure.