Distinctness of the Eigenvalues of a Quadratic form in a Multivariate Sample

作者：Masashi Okamoto · 发表于：The Annals of Statistics · 年份：1973 · DOI：10.1214/aos/1176342472 · 被引用次数：183 · 研究领域：Bayesian Methods and Mixture Models、Morphological variations and asymmetry、Mathematical Dynamics and Fractals

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.