## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 31, Number 1 (1960), 151-158.

### The Distribution of the Latent Roots of the Covariance Matrix

#### Abstract

The distribution of the latent roots of the covariance matrix calculated from a sample from a normal multivariate population, was found by Fisher [3], Hsu [6] and Roy [10] for the special, but important case when the population covariance matrix is a scalar matrix, $\Sigma = \sigma^2I$. By use of the representation theory of the linear group, we are able to obtain the general distribution for arbitrary $\Sigma$.

#### Article information

**Source**

Ann. Math. Statist. Volume 31, Number 1 (1960), 151-158.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177705994

**Digital Object Identifier**

doi:10.1214/aoms/1177705994

**Mathematical Reviews number (MathSciNet)**

MR126901

**Zentralblatt MATH identifier**

0201.52401

**JSTOR**

links.jstor.org

#### Citation

James, Alan T. The Distribution of the Latent Roots of the Covariance Matrix. Ann. Math. Statist. 31 (1960), no. 1, 151--158. doi:10.1214/aoms/1177705994. https://projecteuclid.org/euclid.aoms/1177705994