## The Annals of Statistics

- Ann. Statist.
- Volume 1, Number 4 (1973), 763-765.

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

#### Abstract

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.

#### Article information

**Source**

Ann. Statist., Volume 1, Number 4 (1973), 763-765.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176342472

**Digital Object Identifier**

doi:10.1214/aos/1176342472

**Mathematical Reviews number (MathSciNet)**

MR331643

**Zentralblatt MATH identifier**

0261.62043

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62H10: Distribution of statistics

Secondary: 62E15: Exact distribution theory

**Keywords**

Distinctness of eigenvalues quadratic form in a multivariate sample

#### Citation

Okamoto, Masashi. Distinctness of the Eigenvalues of a Quadratic form in a Multivariate Sample. Ann. Statist. 1 (1973), no. 4, 763--765. doi:10.1214/aos/1176342472. https://projecteuclid.org/euclid.aos/1176342472